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six years after the financial crisis of 2007 - 2008 , millions of households worldwide are still struggling to recover from the aftermath of those traumatic events . the majority of losses are indirect , such as people losing homes or jobs , and for the majority , income levels have dropped substantially . for the economy as a whole , and for households and for public budgets , the miseries of the market meltdown of 2007 - 2008 are not yet over.as a consequence , a consensus for the need for new financial regulation is emerging @xcite . future financial regulation should be designed to mitigate risks within the financial system as a whole , and should specifically address the issue of systemic risk ( sr ) . sr is the risk that the financial system as a whole , or a large fraction thereof , can no longer perform its function as a credit provider , and as a result collapses . in a narrow sense , it is the notion of contagion or impact from the failure of a financial institution or group of institutions on the financial system and the wider economy @xcite . generally , it emerges through one of two mechanisms , either through interconnectedness or through the synchronization of behavior of agents ( fire sales , margin calls , herding ) . the latter can be measured by a potential capital shortfall during periods of synchronized behavior where many institutions are simultaneously distressed @xcite . measures for a potential capital shortfall are closely related to the leverage of financial institutions @xcite . interconnectedness is a consequence of the network nature of financial claims and liabilities @xcite . several studies indicate that financial network measures could potentially serve as early warning indicators for crises @xcite . in addition to constraining the ( potentially harmful ) bilateral exposures of financial institutions , there are essentially two options for future financial regulation to address the problem @xcite : first , financial regulation could attempt to reduce the financial fragility of `` super - spreaders '' or _ systemically important financial institutions _ ( sifis ) , i.e. limiting a potential capital shortfall . this can achieved by reducing the leverage or increasing the capital requirements for sifis . `` super - spreaders '' are institutions that are either too big , too connected or otherwise too important to fail . however , a reduction of leverage simultaneously reduces efficiency and can lead to pro - cyclical effects @xcite . second , future financial regulation could attempt strengthening the financial system as a whole . it has been noted that different financial network topologies have different probabilities for systemic collapse @xcite . in this sense the management of sr is reduced to the technical problem of re - shaping the topology of financial networks @xcite . the basel committee on banking supervision ( bcbs ) recommendation for future financial regulation for sifis is an example of the first option . the basel iii framework recognizes sifis and , in particular , global and domestic systemically important banks ( g - sibs or d - sibs ) . the bcbs recommends increased capital requirements for sifis  the so called `` sifi surcharges '' @xcite . they propose that sr should be measured in terms of the impact that a bank s failure can have on the global financial system and the wider economy , rather than just the risk that a failure could occur . therefore they understand sr as a global , system - wide , loss - given - default ( lgd ) concept , as opposed to a probability of default ( pd ) concept . instead of using quantitative models to estimate sr , basel iii proposes an indicator - based approach that includes the size of banks , their interconnectedness , and other quantitative and qualitative aspects of systemic importance . there is not much literature on the problem of dynamically re - shaping network topology so that networks adapt over time to function optimally in terms of stability and efficiency . a major problem in nw - based sr management is to provide agents with incentives to re - arrange their local contracts so that global ( system - wide ) sr is reduced . recently , it has been noted empirically that individual transactions in the interbank market alter the sr in the total financial system in a measurable way @xcite . this allows an estimation of the marginal sr associated with financial transactions , a fact that has been used to propose a tax on systemically relevant transactions @xcite . it was demonstrated with an agent - based model ( abm ) that such a tax  the _ systemic risk tax _ ( srt )  is leading to a dynamical re - structuring of financial networks , so that overall sr is substantially reduced @xcite .    in this paper we study and compare the consequences of two different options for the regulation of sr with an abm . as an example for the first option we study basel iii with capital surcharges for g - sibs and compare it with an example for the second option  the srt that leads to a self - organized re - structuring of financial networks . a number of abms have been used recently to study interactions between the financial system and the real economy , focusing on destabilizing feedback loops between the two sectors @xcite . we study the different options for the regulation of sr within the framework of the crisis macro - financial model . in this abm , we implement both the basel iii indicator - based measurement approach , and the increased capital requirements for g - sibs . we compare both to an implementation of the srt developed in @xcite . we conduct three `` computer experiments '' with the different regulation schemes . first , we investigate which of the two options to regulate sr is superior . second , we study the effect of increased capital requirements , the `` surcharges '' , on g - sibs and the real economy . third , we clarify to what extend the basel iii indicator - based measurement approach really quantifies sr , as indented by the bcbs . the basel iii indicator - based measurement approach consists of five broad categories : size , interconnectedness , lack of readily available substitutes or financial institution infrastructure , global ( cross - jurisdictional ) activity and `` complexity '' . as shown in [ indicator ] , the measure gives equal weight to each of the five categories . each category may again contain individual indicators , which are equally weighted within the category . p5 cm p7 cm p3 cm category ( and weighting ) & individual indicator & indicator weighting + cross - jurisdictional activity ( 20% ) & cross - jurisdictional claims & 10% + & cross - jurisdictional liabilities & 10% + size ( 20% ) & total exposures as defined for use in the basel iii leverage ratio & 20% + interconnectedness ( 20% ) & intra - financial system assets & 6.67% + & intra - financial system liabilities & 6.67% + & securities outstanding & 6.67% + substitutability / financial institution infrastructure ( 20% ) & assets under custody & 6.67% + & payments activity & 6.67% + & underwritten transactions in debt and equity markets & 6.67% + complexity ( 20% ) & notional amount of over - the - counter ( otc ) derivatives & 6.67% + & level 3 assets & 6.67% + & trading and available - for - sale securities & 6.67%    here below we describe each of the categories in more detail .    this indicator captures the global `` footprint '' of banks . the motivation is to reflect the coordination difficulty associated with the resolution of international spillover effects . it measures the bank s cross - jurisdictional activity relative to other banks activities . here it differentiates between    [ ( i ) ]    cross - jurisdictional claims , and    cross - jurisdictional liabilities . this indicator reflects the idea that size matters . larger banks are more difficult to replace and the failure of a large bank is more likely to damage confidence in the system . the indicator is a measure of the normalized total exposure used in basel iii leverage ratio . a bank s systemic impact is likely to be related to its interconnectedness to other institutions via a network of contractual obligations . the indicator differentiates between    [ ( i ) ]    in - degree on the network of contracts    out - degree on the network of contracts , and    outstanding securities . the indicator for this category captures the increased difficulty in replacing banks that provide unique services or infrastructure . the indicator differentiates between    [ ( i ) ]    assets under custody    payment activity , and    underwritten transactions in debt and equity markets . banks are complex in terms of business structure and operational `` complexity '' . the costs for resolving a complex bank is considered to be greater . this is reflected in the indicator as    [ ( i ) ]    notional amount of over - the - counter derivatives    level 3 assets , and    trading and available - for - sale securities . the score @xmath0 of the basel iii indicator - based measurement approach for each bank @xmath1 and each indicator @xmath2 , e.g. cross - jurisdictional claims , is calculated as the fraction of the individual banks with respect to all @xmath3 banks and then weighted by the indicator weight ( @xmath4 ) . the score is given in basis points ( factor @xmath5 ) @xmath6 where @xmath7 is the set of indicators @xmath2 and @xmath4 the weights from [ indicator ] . p3 cm p3 cm p3 cm p6 cm bucket & score range & bucket thresholds & higher loss absorbency requirement ( common equity as a percentage of risk - weighted assets ) + 5 & d - e & 530 - 629 & 3.50% + 4 & c - d & 430 - 529 & 2.50% + 3 & b - c & 330 - 429 & 2.00% + 2 & a - b & 230 - 329 & 1.50% + 1 & cutoff point - a & 130 - 229 & 1.00%    in the basel iii `` bucketing approach '' , based on the scores from [ score ] , banks are divided into four equally sized classes ( buckets ) of systemic importance , seen here in [ buckets ] . the cutoff score and bucket thresholds have been calibrated by the bcbs in such a way that the magnitude of the higher loss absorbency requirements for the highest populated bucket is 2.5% of risk - weighted assets , with an initially empty bucket of 3.5% of risk - weighted assets . the loss absorbency requirements for the lowest bucket is 1% of risk - weighted assets . the loss absorbency requirement is to be met with common equity @xcite . bucket five will initially be empty . as soon as the bucket becomes populated , a new bucket will be added in such a way that it is equal in size ( scores ) to each of the other populated buckets and the minimum higher loss absorbency requirement is increased by 1% of risk - weighted assets . we use an abm , linking the financial and the real economy . the model consists of banks , firms and households . one pillar of the model is a well - studied macroeconomic model @xcite , the second pillar is an implementation of an interbank market . in particular , we extend the model used in @xcite with an implementation of the basel iii indicator - based measurement approach and capital surcharges for sibs . for a comprehensive description of the model , see @xcite . the agents in the model interact on four different markets . [ ( i ) ]    firms and banks interact on the credit market , generating flows of loan ( re)payments . banks interact with other banks on the interbank market , generating flows of interbank loan ( re)payments . households and firms interact on the labour market , generating flows wage payments . households and firms interact on the consumption - goods market , generating flows of goods . banks hold all of firms and households ? cash as deposits . households are randomly assigned as owners of firms and banks ( share - holders ) . agents repeat the following sequence of decisions at each time step :    firms define labour and capital demand ,    banks rise liquidity for loans ,    firms allocate capital for production ( labour ) ,    households receive wages , decide on consumption and savings ,    firms and banks pay dividends , firms with negative cash go bankrupt ,    banks and firms repay loans ,    illiquid banks try to rise liquidity , and if unsuccessful , go bankrupt .    households which own firms or banks use dividends as income , all other households use wages . banks and firms pay @xmath8 of their profits as dividends . the agents are described in more detail below . there are @xmath9 households in the model . households can either be workers or investors that own firms or banks . each household @xmath1 has a personal account @xmath10 at one of the @xmath3 banks , where index @xmath1 represents the household and index @xmath11 the bank . workers apply for jobs at the @xmath12 different firms . if hired , they receive a fixed wage @xmath13 per time step , and supply a fixed labour productivity @xmath14 . a household spends a fixed percentage @xmath15 of its current account on the consumption goods market . they compare prices of goods from @xmath16 randomly chosen firms and buy the cheapest . there are @xmath12 firms in the model . they produce perfectly substitutable goods . at each time step firm @xmath17 computes its own expected demand @xmath18 and price @xmath19 . the estimation is based on a rule that takes into account both excess demand / supply and the deviation of the price @xmath20 from the average price in the previous time step @xcite . each firm computes the required labour to meet the expected demand . if the wages for the respective workforce exceed the firm s current liquidity , the firm applies for a loan . firms approach @xmath21 randomly chosen banks and choose the loan with the most favorable rate . if this rate exceeds a threshold rate @xmath22 , the firm only asks for @xmath23 percent of the originally desired loan volume . based on the outcome of this loan request , firms re - evaluate the necessary workforce , and hire or fire accordingly . firms sell the produced goods on the consumption goods market . firms go bankrupt if they run into negative liquidity . each of the bankrupted firms debtors ( banks ) incurs a capital loss in proportion to their investment in loans to the company . firm owners of bankrupted firms are personally liable . their account is divided by the debtors _ pro rata_. they immediately ( next time step ) start a new company , which initially has zero equity . their initial estimates for demand @xmath18 and price @xmath19 is set to the respective averages in the goods market . the model involves @xmath3 banks . banks offer firm loans at rates that take into account the individual specificity of banks ( modeled by a uniformly distributed random variable ) , and the firms creditworthiness . firms pay a credit risk premium according to their creditworthiness that is modeled by a monotonically increasing function of their financial fragility @xcite . banks try to grant these requests for firm loans , providing they have enough liquid resources . if they do not have enough cash , they approach other banks in the interbank market to obtain the necessary amount . if a bank does not have enough cash and can not raise the total amount requested on the interbank market , it does not pay out the loan . interbank and firm loans have the same duration . additional refinancing costs of banks remain with the firms . each time step firms and banks repay @xmath24 percent of their outstanding debt ( principal plus interest ) . if banks have excess liquidity they offer it on the interbank market for a nominal interest rate . the interbank relation network is modeled as a fully connected network and banks choose the interbank offer with the most favorable rate . interbank rates @xmath25 offered by bank @xmath17 to bank @xmath1 take into account the specificity of bank @xmath17 , and the creditworthiness of bank @xmath1 . if a firm goes bankrupt the respective creditor bank writes off the respective outstanding loans as defaulted credits . if the bank does not have enough equity capital to cover these losses it defaults . following a bank default an iterative default - event unfolds for all interbank creditors . this may trigger a cascade of bank defaults . for simplicity s sake , we assume a recovery rate set to zero for interbank loans . this assumption is reasonable in practice for short term liquidity @xcite . a cascade of bankruptcies happens within one time step . after the last bankruptcy is resolved the simulation is stopped .      in the abm , we implement the size indicator by calculating the total exposures of banks . total exposure includes all assets of banks excluding cash , i.e. loans to firms and loans to other banks . interconnectedness is measured in the model by interbank assets ( loans ) and interbank liabilities ( deposits ) of banks . as a measure for substitutability we use the payment activity of banks . the payment activity is measured by the sum of all outgoing payments by banks . in the model we do not have cross - jurisdictional activity and banks are not engaged in selling complex financial products including derivatives and level 3 assets . we therefore set the weights for global ( cross - jurisdictional ) activity and complexity to zero . banks in the model have to observe loss absorbency ( capital ) requirements according to basel iii . they are required to hold 4.5% of common equity ( up from 2% in basel ii ) of risk - weighted assets ( rwas ) . rwas are calculated according to the standardized approach , i.e. with fixed weights for all asset classes . as fixed weights we use 100% for interbank loans and commercial loans . we define equity capital of banks in the model as common equity .    in the model banks are allocated to the five buckets shown in [ buckets ] based on the scores obtained by [ score ] . banks have to meet additional loss absorbency requirements as shown in [ buckets ] . the score is calculated at every time step @xmath26 and capital requirements must be observed before providing new loans . the srt is implemented in the model as described in @xcite , for details see [ srt ] and @xcite . the srt is calculated according to [ srteq_simple ] and is imposed on all interbank transactions . all other transactions are exempted from srt . before entering a desired loan contraction , loan requesting bank @xmath17 obtains quotes for the srt rates from the central bank , for various potential lenders @xmath1 . bank @xmath17 chooses the interbank offer from bank @xmath1 with the smallest total rate . the srt is collected into a bailout fund . below we present the results of three experiments . the first experiment focuses on the performance of different options for regulation of sr , the second experiment on the consequences of different capital surcharges for g - sibs , and the third experiment on the effects of different weight distributions for the basel iii indicator - based measurement approach .              in order to understand the effects of basel iii capital surcharges for g - sibs on the financial system and the real economy , and to compare it with the srt , we conduct an experiment where we consider three cases :    [ ( i ) ]    financial system regulated with basel ii ,    financial system regulated with basel iii , with capital surcharges for g - sibs ,    financial system with the srt .    with basel ii we require banks to hold 2% of common equity of their rwas . rwas are calculated according to the standardized approach . the effects of the different regulation policies on total losses to banks @xmath27 ( see [ risk_measures ] ) are shown in [ fig : regulation_type](a ) . clearly , with basel ii ( red ) fat tails in the loss distributions of the banking sector are visible . basel iii with capital surcharges for g - sibs slightly reduces the losses ( almost not visible ) . the srt gets almost completely rid of big losses in the system ( green ) . this reduction in major losses in the financial system is due to the fact that with the srt the possibility of cascading failure is drastically reduced . this is shown in [ fig : regulation_type](b ) where the distributions of cascade sizes @xmath28 ( see [ risk_measures ] ) for the three modes are compared . with the basel regulation policies we observe cascade sizes of up to @xmath29 banks , while with the srt the possibility of cascading failure is drastically reduced . clearly , the total transaction volume @xmath30 ( see [ risk_measures ] ) in the interbank market is not affected by the different regulation policies . this is seen in [ fig : regulation_type](c ) , where we show the distributions of transaction volumes .    in [ fig : regulation_type](d ) we show the _ sr - profile _ of the financial system given by the rank - ordered debtranks @xmath31 of all banks @xcite . the sr - profile shows the distribution of systemic impact across banks in the financial system . the bank with the highest systemic impact is to the very left . obviously , the srt drastically reduces the systemic impact of individual banks and leads to a more homogeneous spreading of sr across banks . basel iii with capital surcharges for g - sibs sees a slight reduction in the systemic impact of individual banks . next , we study the effect of different levels of capital surcharges for g - sibs . here we consider three different settings :    [ ( i ) ]    capital surcharges for g - sibs as specified in basel iii ( [ buckets ] ) ,    double capital surcharges for g - sibs ,    threefold capital surcharges for g - sibs .    with larger capital surcharges for g - sibs , we observe a stronger effect of the basel iii regulation policy on the financial system . clearly , the shape of the distribution of losses @xmath27 is similar ( [ fig : surcharges](a ) ) . the tail of the distributions is only reduced due to a decrease in efficiency ( transaction volume ) , as is seen in [ fig : surcharges](c ) . evidently , average losses @xmath27 are reduced at the cost of a loss of efficiency by roughly the same factor . this means that basel iii must reduce efficiency in order to show any effect in terms of sr , see [ discussion ] .    in [ fig : surcharges](d ) we show the sr - profile for different capital surcharges for g - sibs . clearly , the systemic impact of individual banks is also reduced at the cost of a loss of efficiency by roughly the same factor .    in [ fig : surcharges](b ) we show the cascade size of synchronized firm defaults . here we see an increase in cascading failure of firms with increasing capital surcharges for g - sibs . this means larger capital surcharges for g - sibs can have pro - cyclical side effects , see [ discussion ] .            finally , we study the effects of different weight distributions for the basel iii indicator - based measurement approach . in particular , we are interested in whether it is more effective to have capital surcharges for `` super - spreaders '' or for `` super - vulnerable '' financial institutions . a vulnerable financial institution in this context is an institution that is particularly exposed to failures in the financial system , i.e. has large credit or counterparty risk ( cr ) . holding assets is generally associated with the risk of losing the value of an investment . whereas a liability is an obligation towards a counterparty that can have an impact if not fulfilled . to define an indicator that reflects sr and identifies `` super - spreaders '' we set the weight on intra - financial system liabilities to 100% . for an indicator that reflects cr of interbank assets and identifies vulnerable financial institutions of we set the weight on intra - financial system assets to 100% . weights on all other individual indicators are set to zero . specifically , we consider three different weight distributions . [ ( i ) ]    weights as specified in basel iii ( [ indicator ] ) ,    indicator weight on interbank liabilities set to 100% ,    indicator weight on interbank assets set to 100% .    to illustrate the effects of different weight distributions , we once again use larger capital surcharges for g - sibs , as specified in basel iii . to allow a comparison between the different weight distributions , we set the level of capital surcharges for each weight distribution to result in a similar level of efficiency ( credit volume ) . specifically , for the weight distribution as specified in basel iii ( [ indicator ] ) we multiply the capital surcharges for g - sibs as specified in basel iii ( [ buckets ] ) by a factor @xmath32 , for indicator weight on interbank liabilities by @xmath33 and for indicator weight on interbank assets by @xmath34 . in [ fig : weights](b ) we show that efficiency , as measured by transaction volume in the interbank market , is indeed similar for all weight distributions .    in [ fig : weights](a ) we show the losses to banks @xmath27 for the different weight distributions . clearly , imposing capital surcharges on `` super - spreaders '' ( yellow ) does indeed reduce the tail of the distribution , but does not , however , get completely rid of large losses in the system ( yellow ) . in contrast , imposing capital surcharges on `` super - vulnerable '' financial institutions ( red ) shifts the mode of the loss distribution without reducing the tail , thus making medium losses more likely without getting rid of large losses .    to illustrate the effect of the different weight distributions , we show the risk profiles for sr and cr . risk profiles for sr show the systemic impact as given by the debtrank @xmath35 ( banks are ordered by @xmath35 , the most systemically important being to the very left ) . risk profiles for cr show the distribution of _ average vulnerability _ , i.e. a measure for cr in a financial network , for details see [ vulnerability_section ] . the corresponding sr- and cr - profiles are shown for the different weight distributions in [ fig : weights](c ) and [ fig : weights](d ) . imposing capital surcharges on `` super - spreaders '' leads to a more homogeneous spreading of sr across all agents , as shown in [ fig : weights](c ) ( yellow ) . whereas capital surcharges for `` super - vulnerable '' financial institutions leads to a more homogeneous spreading of cr ( [ fig : weights](d ) ( red ) ) . interestingly , homogeneous spreading of cr ( sr ) leads to a more unevenly distributed sr ( cr ) , as seen by comparing [ fig : weights](c ) and [ fig : weights](d ) . we use an abm to study and compare the consequences of the two different options for the regulation of sr . in particular we compare financial regulation that attempts to reduce the financial fragility of sifis ( basel iii capital surcharges for g - sibs ) with a regulation policy that aims directly at reshaping the topology of financial networks ( srt ) . sr emerges in the abm through two mechanisms , either through interconnectedness of the financial system or through synchronization of the behavior of agents . cascading failure of banks in the abm can be explained as follows . triggered by a default of a firm on a loan , a bank may suffer losses exceeding its absorbance capacity . the bank fails and due to its exposure on the interbank market , other banks may fail as well . cascading failure can be seen in [ fig : regulation_type](b ) . basel iii capital surcharges for g - sibs work in the abm as follows . demand for commercial loans from firms depends mainly on the expected demand for goods . firms approach different banks for loan requests . if banks have different capital requirements , banks with lower capital requirements may have a higher leverage and provide more loans . effectively , different capital requirement produce inhomogeneous leverage levels in the banking system . imposing capital surcharges for g - sibs means that banks with a potentially large impact on others must have sizable capital buffers . with capital surcharges for g - sibs , non - important banks can use higher leverage until they become systemically important themselves . this leads to a more homogenous spreading of sr , albeit that reduction and mitigation of sr is achieved `` indirectly '' . the srt leads to a self - organized reduction of sr in the following way @xcite : banks looking for credit will try to avoid this tax by looking for credit opportunities that do not increase sr and are thus tax - free . as a result , the financial network rearranges itself toward a topology that , in combination with the financial conditions of individual institutions , will lead to a new topology where cascading failures can no longer occur . the reduction and mitigation of sr is achieved `` directly '' by re - shaping the network .    from the experiments we conclude that basel iii capital surcharges for g - sibs reduce and mitigate sr at the cost of a loss of efficiency of the financial system ( [ fig : surcharges](a ) and [ fig : surcharges](c ) ) . this is because overall leverage is reduced by capital surcharges . on the other hand , the srt keeps the efficiency comparable to the unregulated financial system . however it avoids cascades due to the emergent network structure . this means  potentially much higher  capital requirements for `` super - spreaders '' do address sr but at the cost of efficiency . sr through synchronization emerges in the abm in the following way : similarly to the root cause of cascading failure in the banking system , an initial shock from losses from commercial loans can lead to a synchronization of firm defaults . if banks are able to absorb initial losses , the losses still result in an implicit increase in leverage . in order to meet capital requirements ( basel iii ) , the bank needs to reduce the volume of commercial loans . this creates a feedback effect of firms suffering from reduced liquidity , which in turn increases the probability of defaults and closes the cycle . this feedback effect is inherent to the system and can be re - inforced by basel iii capital surcharges for g - sibs . in the experiments we see that this feedback effect gets more pronounced with larger capital surcharges for g - sibs ( [ fig : surcharges](b ) ) . here we see an increase in cascading failure of firms with increasing capital surcharges for g - sibs . this means capital surcharges for g - sibs can have pro - cyclical side effects . basel iii measures systemic importance with an indicator - based measurement approach . the indicator approach is based on several individual indicators consisting of banks assets and liabilities . by studying the effect of different weight distributions for the individual indicators , we find that basel iii capital surcharges for g - sibs are more effective with higher weights on liabilities ( [ fig : weights](a ) ) . this means quite intuitively  that asset - based indicators are more suitable for controlling credit risk and liability based indicators are more suitable for controlling systemic risk . since the indicators in the basel proposal are predominantly based on assets , the basel iii indicator - based measurement approach captures predominantly credit risk and therefore does not meet it s declared objective .    to conclude with a summary at a very high level , the policy implications obtained with the abm are [ ( i ) ]    re - shaping financial networks is more effective and efficient than reducing leverage ,    capital surcharges for g - sibs ( `` super - spreaders '' ) can reduce sr ,    but must be larger than specified in basel iii to have an measurable impact ,    and thus cause a loss of efficiency . basel iii capital surcharges for g - sibs can have pro - cyclical side effects . debtrank is a recursive method suggested in @xcite to determine the systemic relevance of nodes in financial networks . it is a number measuring the fraction of the total economic value in the network that is potentially affected by a node or a set of nodes . @xmath36 denotes the interbank liability network at any given moment ( loans of bank @xmath1 to bank @xmath17 ) , and @xmath37 is the capital of bank @xmath17 . if bank @xmath17 defaults and can not repay its loans , bank @xmath1 loses the loans @xmath36 . if @xmath1 does not have enough capital available to cover the loss , @xmath1 also defaults . the impact of bank @xmath17 on bank @xmath1 ( in case of a default of @xmath17 ) is therefore defined as @xmath38 \quad.\ ] ] the value of the impact of bank @xmath17 on its neighbors is @xmath39 . the impact is measured by the _ economic value _ @xmath40 of bank @xmath17 . for the economic value we use two different proxies . given the total outstanding interbank exposures of bank @xmath17 , @xmath41 , its economic value is defined as @xmath42 to take into account the impact of nodes at distance two and higher , this has to be computed recursively . if the network @xmath43 contains cycles , the impact can exceed one . to avoid this problem an alternative was suggested in @xcite , where two state variables , @xmath44 and @xmath45 , are assigned to each node . @xmath46 is a continuous variable between zero and one ; @xmath47 is a discrete state variable for three possible states , undistressed , distressed , and inactive , @xmath48 . the initial conditions are @xmath49 , and @xmath50 ( parameter @xmath51 quantifies the initial level of distress : @xmath52 $ ] , with @xmath53 meaning default ) . the dynamics of @xmath54 is then specified by @xmath55 \quad.\ ] ] the sum extends over these @xmath1 , for which @xmath56 , @xmath57 the debtrank of the set @xmath58 ( set of nodes in distress at time @xmath59 ) , is @xmath60 , and measures the distress in the system , excluding the initial distress . if @xmath58 is a single node , the debtrank measures its systemic impact on the network . the debtrank of @xmath58 containing only the single node @xmath17 is @xmath61 the debtrank , as defined in [ debtrank ] , excludes the loss generated directly by the default of the node itself and measures only the impact on the rest of the system through default contagion . for some purposes , however , it is useful to include the direct loss of a default of @xmath17 as well . the total loss caused by the set of nodes @xmath58 in distress at time @xmath59 , including the initial distress is @xmath62      the precise meaning of the debtrank allows us to define the _ expected systemic loss _ for the entire economy @xcite . assuming that we have @xmath3 banks in the system , the expected systemic loss can be approximated by @xmath63 with @xmath19 the probability of default of node @xmath17 , and @xmath64 the combined economic value of all nodes at time @xmath26 . for details and the derivation , see @xcite .    to calculate the marginal contributions to the expected systemic loss , we start by defining the _ net liability network _ @xmath65 $ ] . after we add a specific liability @xmath66 , we denote the liability network by @xmath67 where @xmath68 is the kronecker symbol . the marginal contribution of the specific liability @xmath66 on the expected systemic loss is @xmath69 where @xmath70 is the debtrank of the liability network and @xmath71 the total economic value with the added liability @xmath66 . clearly , a positive @xmath72 means that @xmath66 increases the total sr . finally , the marginal contribution of a single loan ( or a transaction leading to that loan ) can be calculated . we denote a loan of bank @xmath17 to bank @xmath1 by @xmath73 . the liability network changes to @xmath74 since @xmath17 and @xmath1 can have a number of loans at a given time @xmath26 , the index @xmath75 numbers a specific loan between @xmath17 and @xmath1 . the marginal contribution of a single loan ( transaction ) @xmath76 , is obtained by substituting @xmath77 by @xmath78 in [ marginal_effect ] . in this way every existing loan in the financial system , as well as every hypothetical one , can be evaluated with respect to its marginal contribution to overall sr . the central idea of the srt is to tax every transaction between any two counterparties that increases sr in the system @xcite . the size of the tax is proportional to the increase of the expected systemic loss that this transaction adds to the system as seen at time @xmath26 . the srt for a transaction @xmath79 between two banks @xmath17 and @xmath1 is given by @xmath80 \quad . \label{srteq_simple } \end{gathered}\ ] ] @xmath81 is a proportionality constant that specifies how much of the generated expected systemic loss is taxed . @xmath82 means that 100% of the expected systemic loss will be charged . @xmath83 means that only a fraction of the true sr increase is added on to the tax due from the institution responsible . for details , see @xcite .      using debtrank we can also define an _ average vulnerability _ of a node in the liability network @xmath36 @xcite . recall that @xmath84 is the state variable , which describes the health of a node in terms of equity capital after @xmath85 time steps ( @xmath86 , i.e. all nodes are either undistressed or inactive ) . when calculating @xmath84 for @xmath87 containing only a single node @xmath17 , we can define @xmath88 as the health of bank @xmath1 in case of default of bank @xmath17 @xmath89 note that is necessary to simulate the default of every single node of the liability network @xmath36 separately to obtain @xmath90 . with @xmath90 we can define the average vulnerability of a node in the liability network as the average impact of other nodes on node @xmath17 @xmath91 where @xmath3 is the number of nodes in the liability network @xmath36 . we use the following three observables : ( 1 ) the size of the cascade , @xmath92 as the number of defaulting banks triggered by an initial bank default ( @xmath93 ) 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in addition to constraining bilateral exposures of financial institutions , there are essentially two options for future financial regulation of systemic risk ( sr ) : first , financial regulation could attempt to reduce the financial fragility of global or domestic systemically important financial institutions ( g - sibs or d - sibs ) , as for instance proposed in basel iii . 
 second , future financial regulation could attempt strengthening the financial system as a whole . 
 this can be achieved by re - shaping the topology of financial networks . 
 we use an agent - based model ( abm ) of a financial system and the real economy to study and compare the consequences of these two options . by conducting three `` computer experiments '' with the abm we find that re - shaping financial networks 
 is more effective and efficient than reducing leverage . capital surcharges for g - sibs can reduce sr , but must be larger than those specified in basel iii in order to have a measurable impact . 
 this can cause a loss of efficiency . 
 basel iii capital surcharges for g - sibs can have pro - cyclical side effects .