Papers by Todd R. Kaplan

It is proved for two-player normal form games that if a totally mixed Nash equilibrium exists then the entire set of Nash equilibria is (trembling-hand) perfect. More generally, it is proved that if there is a (trembling-hand) perfect equilibrium, then all Nash equilibria whose supports are contained in the perfect equilibrium's support are also perfect. The possibility of similar relationships in three or more player games and proper equilibria of two-player games is discussed.

We describe two-person simultaneous play games. First, we use a zero sum game to illustrate minimax, dominant and best response strategies. We illustrate Nash Equilbria in the Prisoner's Dilemma and the Battle of the Sexes Game, and distinguish three types of Nash Equilibria: a pure strategy, a mixed strategy, and a continuum (partially) mixed strategy. Then we introduce the program, Nash.m and use it to solve the games. We display the full code of Nash.m, and finally we discuss the performance characteristics of Nash.m.

I present an example showing it is sometimes efficient for a bank to commit to a policy that keeps information about its risky assets private. Current practices in banking result in bankers having private information: demand deposits are non-contingent contracts, there are time lags before the public has access to updated balance sheets, and certain items on a bank's balance sheet are marked at book-value rather than market-value. The Savings & Loan failures in the 1980's have led to an increase in banking legislation such as the FIRREA of 1989 and the FDICIA of 1991. These laws affect the release of information about a bank's assets by creating a minimum capital requirement, imposing a new examination standard for banks' assets, and implementing a risk-based insurance scheme.

My model, which is based upon the Diamond and Dybvig [1983] model, has the feature that banks acquire information about their risky assets before depositors acquire it. Banks have the option of revealing this information by using contingent contracts (a policy that would be efficient without private information). I present specifications of depositors' preferences and bankers' technology for which a bank would not want to use this option. In these cases, information should be kept secret. Although this analysis abstracts from the moral hazard problem that recent laws were meant to reduce, it demonstrates a potential danger of the increased regulation in banking. The model also shows that if a partial suspension reveals information about a bank's assets, then sometimes the suspension scheme is inefficient. This contrasts with recent literature (Gorton [1985a], Wallace [1990]).

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