Microeconomic rationale for UIP (uncovered interest rate parity) The key idea behind UIP is that as for all common financial instruments, the &quot;law of no free lunch&quot; should also hold for currencies. However it differs from traditional replication-based no-arbitrage conditions like CIP in that there is no obvious argument for why the exploitation of opportunities when it does not hold true necessarily depletes all such opportunities, thereby making &quot;free lunches&quot; rare in a world of rational investors.
Concretely, the currency of a country with a relatively higher interest rate needs to gradually depreciate to offset the positive earnings potential. What mechanism drives this gradual depreciation?
I've heard that there are models on this issue but have not been able to locate the literature.
Thanks for all suggestions!
There is an arbitrage argument for UIP because under UIP forward rate must be equal to expected exchange rate so the same arbitrage arguments from CIP can be extended to UIP (under its strict assumptions). You will find it in most international macroeconomics or finance textbooks. For example, according to Nelson Mark's International Macroeconomics and Finance:

If foreign exchange participants are risk neutral, they
care only about the mean value of asset returns and do not care at all
about the variance of returns. Risk-neutral individuals are also willing to take unboundedly large positions on bets that have a positive
expected value. Since $F_{t} − S_{t+1}$ is the profit from taking a position in
forward foreign exchange, under risk-neutrality expected forward speculation profits are driven to zero and the forward exchange rate must,
in equilibrium, be market participant's expected future spot exchange
rate
$$F_{t} = E_{t}(S_{t+1}). (1.6)$$
Substituting (1.6) into (1.2) [result given from covered interest parity where instead of expected exchange rate you have forward rate] gives the uncovered interest parity condition
$$ 1 + i_t = (1 + i_t^* )\frac{E_t[S_{t+1}]}{S_t}. (1.7)$$
If (1.7) is violated, a zero-net investment strategy of borrowing in one
currency and simultaneously lending uncovered in the other currency has a positive payoff in expectation. We use the uncovered interest
parity condition as a first-approximation to characterize international
asset market equilibrium, especially in conjunction with the monetary
model (chapters 3, 10, and 11). However, as you will see in chapter 6,
violations of uncovered interest parity are common and they present an
important empirical puzzle for international economists.

The in text square brackets contain my clarifications. So as the above passages show there is an arbitrage argument in UIP. You can find further sources and more detailed explanations in the textbook itself.