This paper considers a problem faced by players who are involved in a sequence of games: not necessarily the same games, not necessarily with the same opponents, and not necessarily under conditions of complete information. The players are assumed to act in response to stationary Markovian hypotheses which they form about the actions of their opponents. Conditions are explored which require that these hypotheses be correct on average and that the players actions be optimal in response to their hypotheses.

[The problem under consideration is to select the smallest majority size such that at least one social state is not defeated by any other when restrictions on possible voters' preferences are explicitly known, and when populations of arbitrary size are possible. This problem is formulated in mathematical programming terms. The special structure of the formulation is discussed, and some results concerning bounds on the majority sizes are established.]

The sovereign-debt literature has often implicitly assumed that all the power in the bargaining game between debtor and creditor lies with the latter. This paper explores that assumption by analyzing three game-theoretic models of debt renegotiations. In two of the models, both of which are built on the traditional one-sector growth model, all the subgame-perfect equilibria have an extreme form in which the game's surplus is captured by the creditor. The third game has many subgame-perfect equilibria that do not have this feature, however. The roles of various assumptions in all three games are examined.

In the mid-1970s several authors studied models of markets with asymmetric information in which equilibria do not exist. Although those authors focused on models of insurance and education, it was recognized that similar nonexistence problems arise in a wide class of models with asymmetric information. Recently, Dasgupta and Maskin have demonstrated that for a game-theoretic version of at least one of those models, although no equilibria may exist in pure strategies, equilibria exist in mixed strategies. In the present paper we construct a mixed-strategy equilibrium for one member of the class—Spence's signalling model of education. Qualitative features of the equilibrium are explored.

IN A STIMULATING RECENT PAPER, Abreu and Matsushima (1992) (hereafter A-M) show how a class of social choice functions can be virtually implemented in iteratively undominated strategies. This work has several important features: the mechanisms used are finite and not too difficult to understand, and so less objectionable in this regard than many in the literature; the class of social choice functions implemented is large; and the solution concept-Nash equilibrium determined uniquely by iterative elimination of strongly dominated strategies-is relatively uncontroversial. The point of this note is to argue that the mechanisms used by A-M unfortunately tend to generate games in which the iterative removal of strongly dominated strategies sometimes is indeed (or ought to be) controversial.2 We proceed by first examining an example of a related but simpler implementation problem in which the argument is easily exposed, then indicating how the argument applies generally in the A-M setup. Consider the following much-discussed two-player coordination game:

In this paper, the authors reexamine the data from B. O'Neill's (1987) experiment involving a repeated, two-person, constant-sum game. They find that there is less evidence in support of the minimax hypothesis than indicated by O'Neill. There is strong evidence of serial correlation in players' choices, with several players displaying statistically significant dependence on the past moves of their opponents. The authors interpret this finding as evidence that the plays themselves rejected minimax play as the appropriate model for their opponents' behavior. They find no evidence that players' behavior approached minimax behavior as players became more experienced.