Ennio Stacchetti

Psychological games and sequential rationality

Abstract In psychological games the payoff to each player depends not only on what every player does but also on what he thinks every player believes, and on what he thinks they believe others believe, and so on. In equilibrium, beliefs are assumed to correspond to reality. Yet psychological games and psychological equilibria allow one to model belief-dependent emotions such as anger and surprise that are problematic for conventional game theory. We are particularly interested in issues of sequential rationality for psychological games. We show that although backward induction cannot be applied, and “perfect” psychological equilibria may not exist, subgame perfect and sequential equilibria always do exist.

Optimal Cartel Equilibria with Imperfect monitoring

There exist optimal symmetric equilibria in the Green-Porter model [5, 8] having an elementary intertemporal structure. Such an equilibrium is described entirely by two subsets of price space and two quantities, the only production levels used by firms in any contingency. The central technique employed in the analysis is the reduction of the repeated game to a family of static games.

The English Auction with Differentiated Commodities

Abstract We study economies (with indivisibilities) that satisfy the gross substitutes (GS) condition. We define an excess demand set with the property that increasing the prices of all goods in excess demand eventually leads to the smallest Walrasian prices. This procedure is a generalization of the auction studied by G. Demange, D. Gale and M. J. Sotomayor, Polit. Econ. 94 (1986), 863–872. In our auction, truthful revelation of demand is a perfect Bayesian equilibrium if the smallest Walrasian prices correspond to the Vickrey–Clarke–Groves payments. However, no dynamic auction can reveal sufficient information to implement the Vickrey mechanism if all GS preferences are allowed. Journal of Economic Literature Classification Numbers: D4, D44, D5, D51.

Sequential equilibria in a Ramsey tax model

This paper presents a full characterization of the equilibrium value set of a Ramsey tax model. More generally, it develops a dynamic programming method for a class of policy games between the government and a continuum of consumers. By selectively incorporating Euler conditions into a strategic dynamic programming framework, we wed two technologies that are usually considered competing alternatives, resulting in a dramatic simplification of the problem.

Analysis of a dynamic, decentralized exchange economy☆

Abstract A model of a dynamic exchange economy is presented. Similarly to the Walrasian equilibrium problem, each consumer is characterized by a feasible set and by an instantaneous demand function, that depends on the price vector, time, and the commodity holding. The commodity holding of each consumer varies, at each moment, according to this instantaneous demand function. We show that the market can choose prices that keep the commodity holding of each consumer within his consumption set, while ensuring that the aggregate commodity holding satisfies the scarcity constraints of the market.

Agency Models With Frequent Actions

The paper analyzes dynamic principal–agent models with short period lengths. The two main contributions are: (i) an analytic characterization of the values of optimal contracts in the limit as the period length goes to 0, and (ii) the construction of relatively simple (almost) optimal contracts for fixed period lengths. Our setting is flexible and includes the pure hidden action or pure hidden information models as special cases. We show how such details of the underlying information structure affect the optimal provision of incentives and the value of the contracts. The dependence is very tractable and we obtain sharp comparative statics results. The results are derived with a novel method that uses a quadratic approximation of the Pareto boundary of the equilibrium value set.