The Evolution of Exchange

The aim of the paper is to introduce the modern techniques of evolutionary game theory introduced into economics by Young (1993) and others to analyze exchange economies. We define a dynamic matching process on the simple housing problem introduced by Shapley and Scarf (1974) and analyze the stochastic stability of its allocations. Our main findings are: 1. All the efficient allocations are stochastically stable. 2. In three-person economies, all the stochastically stable allocations are efficient. 3. An example of a four-agent economy where an inefficient allocation is stochastically stable.

Communication, Credible Improvements and the Core of an Economy with Asymmetric Information

We analyze an economy with asymmetric information and endogenize the possibilities for information transmission between members of a coalition. We then define a concept of the Core that takes into account these communication possibilities. The internal consistency of the improvements is considered and an Internally Consistent Core, which requires credibility from the improvements is introduced.Asymmetric Information; Core; Common Knowledge.

A Remark on Bargaining and Non-Expected Utility

We show that a bargaining game of alternating offers with exogenous risk of breakdown and played by dynamically consistent non-expected utility maximizers is formally equivalent to Rubinstein's (1982) game with time preference. Within this game, the behavior of dynamically consistent players is indistinguishable from the behavior of expected utility maximizers.Bargaining, non-expected utility.

On Risk Aversion and Bargaining Outcomes

We revisit the well known result that asserts that and increase in the degree of one's risk aversion improves the position one's opponents. for this purpose, we apply Yaari's dual theory of choice under risk both to Nash's bargaining problem and to Rubinstein's game of alternating offers. Within this theory and unlike under expected utility, risk aversion influences the bargaining outcome only when this outcome is random, namely, when the players are risk lovers. In this case, an increase in ones degree of risk aversion, increases one's share of the pie.Bargaining; non-expected utility; risk aversion.

In Defense of DEFECT or Cooperation does not Justify the Solution Concept

The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoners' dilemma, when preferences are lexicographic in the complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity.Cooperation; prisoners' dilemma; automata; evolution.

Utility Equivalence in Sealed Bid Auctions and the Dual Theory of Choice Under Risk

This paper analyzes symmetric, single item auctions in the private values framework, with buyers whose preferences satisfy the axioms of Yaari's (1987) dual theory of choice under risk. It is shown that when their valuations are independently and identically distributed, buyers are indifferent among all the auctions contained in a big family of mechanisms which includes the standard auctions. It is also shown that in the linear equilibria of the sealed bid double auction, as the degree of players' risk aversion grows arbitrarily large, the ex post inefficiency of the mechanism tends to vanish.Auctions; non-expected utility; risk aversion.

Mistakes in cooperation: the stochastic stability of edgeworth's recontracting

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes -do not improve- in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process

The Core of Economies with Asymmetric Information: An Axiomatic Approach

We propose two generalizations of the Davis-Maschler reduced game property to economies with asymmetric information and apply them in the characterization of two solution concepts. One is Wilson's (1978) Coarse Core and the other is a subsolution of it which we call the Coarse+ Core.Asymmetric information; core; reduced game property; consistency.

Mistakes in cooperation: the stochastic stability of edgeworth's recontracting.

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes -do not improve- in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process.