Chaotic consumption patterns in a simple2-D addiction model

Summary.  Consumption fluctuations in a simple 2-D addiction model are investigated. The behavioural equations of the model are suggested by a related ‘rational addiction’ model of Becker and Murphy [2]. Our model generates erratic, seemingly unpredictable consumption patterns of the addicted persons. The occurence of chaos is proven by locating a so called horseshoe map in the phase space. Received: April 4, 1994; revised version March 25, 1996     

Cooperative games in permutational structure

Summary. By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition being a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. In this paper we consider non-transferable utility games in which for any coalition the set of payoffs depends on a permutation or ordering upon any partition of the coalition into subcoalitions. We call such a game a cooperative game in permutational structure or shortly permutational game. Doing so we extend the scope of the standard cooperative game theory in dealing with economic or political problems. Next we define the concept of core for such games. By introducing balancedness for ordered partitions of coalitions, we prove the nonemptiness of the core of a balanced non-transferable utility permutational game. Moreover we show that the core of a permutational game coincides with the core of an induced game in coalitional structure, but that balancedness of the permutational game need not imply balancedness of the corresponding coalitional game. This leads to a weakening of the conditions for the existence of a nonempty core of a game in coalitional structure, induced by a game in permutational structure. Furthermore, we refine the concept of core for the class of permutational games. We call this refinement the balanced-core of the game and show that the balanced-core of a balanced permutational game is a nonempty subset of the core. The proof of the nonemptiness of the core of a permutational game is based on a new intersection theorem on the unit simplex, which generalizes the well-known intersection theorem of Shapley. Received: October 31, 1995; revised version: February 5, 1997     

An experimental analysis of the bandit problem

Summary.  We investigate, in an experimental setting, the behavior of single decision makers who at discrete time intervals over an “infinite” horizon may choose one action from a set of possible actions where this set is constant over time, i.e. a bandit problem. Two bandit environments are examined, one in which the predicted behavior should always be myopic (the two-armed bandit) and the other in which the predicted behavior should never be myopic (the one-armed bandit). We also investigate the comparative static predictions as the underlying parameters of the bandit environments are changed. The aggregate results show that the behavior in the two bandit environments are quantitatively different and in the direction of the theoretical predictions. Received: October, 27, 1994; revised version February 27, 1996     

A remark on the equilibrium set of pureexchange economies

Summary.  We present a unified mathematical framework within which, among others, pure exchange economies with a finite set of agents, as well as those with a continuum of traders may be studied simultaneously. We prove that the reasoning presented by Balasko (1975) on the equilibrium set for finite economies generalizes very naturally to our setting. His results may therefore be recovered as a special case of those presented in this note. Received: April 9, 1996; revised version August 19, 1996     

Reallocation of an infinitely divisible good

Summary. We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties. Received: August 29, 1995; revised version June 26, 1996     

Relaxing Pareto optimality in economic environments

Summary.  The individual preference domain is the family of profiles of economic preferences on the set of allocations of public or private goods, or both. The agenda domain assumption allows for a finite lower bound on the size of a feasible set. If a social choice correspondence satisfies nonimposition, Arrow’s choice axiom, and independence of infeasible alternatives then it is directly or inversely dictatorial, or null. Received: October 10, 1995; revised version: June 20, 1996     

Coalitional stability under perfect foresight

Summary. We analyze strategic social environments where coalitions can form through binding or nonbinding agreements and actions of a coalition may impose externalities upon the welfare of the rest of the players. We define a solution concept that (1) captures the perfect foresight of the players that has been overlooked in the literature (e.g., Harsanyi [10] and Chwe [6]) and (2) identifies the coalitions that are likely to form and the “stable” outcomes that will not be replaced by any coalition of rational (and hence farsighted) players. The proposed solution concept thereby offers a notion of agreements and coalition formation in complex social environments. Received: February 12, 1996; revised version: March 3, 1997     

A comparison between the core and the monopoly solutions in a mixed exchange economy

Summary. Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers. Received: March 4, 1996; revised version July 7, 1996     

Asymmetric information, strategic behavior, and discrimination in the labor market

Summary  The neoclassical model of labor market discrimination assumes the presence of either prejudiced preferences, biased assessments of worker productivity, or monopsony power. We show that when market agents control asymmetric information, strategic behavior can induce discriminatory hiring practices even when these market features are absent. Moreover, strategic interaction many distort public policies to the point of harming the segments of the work force they were designed to support. Received: January 3, 1996 revised version April 29, 1996     

Money and specialization

Summary.  This paper examines the relationship between specialization and the use of money in two versions of the search-theoretic monetary model. The first version establishes a surprising result that specialization is more likely to occur in a barter economy than in a monetary economy. The result is reversed in the second version where a different specification of preferences is adopted to limit the scope of barter. This contrast between the results provides a concrete illustration of the general argument that money encourages specialization only when it enlarges the extent of the market. Received: January 31, 1995; revised version August 12, 1996     

Demand fluctuations and capacity utilization under duopoly

Summary.  This paper studies the impact of uncertain demand on firms’ capacity decisions when they operate in an oligopolistic environment. We define a two-stage game where firms choose capacity in the first stage without knowing which state of Nature is going to realize, and output levels in the second, knowing which state is realized. We prove the existence of a symmetric subgame perfect equilibrium at which firms are in excess capacity compared with the capacity they would choose in the Cournot certainty equivalent game. Received: May 17, 1996; revised version July 31, 1996     

Serial cost sharing of excludable public goods: general cost functions

Summary. A group of individuals meet to share the cost and determine output allocations of a partial-excludable public good. We demonstrate that, for general cost functions and preferences that satisfy the Spence-Mirlees sorting condition, the serial cost-sharing formula (Moulin, 1994) has remarkable incentive properties. First, a direct economic mechanism that uses the serial formula is coalition strategy-proof, envy-free and satisfies the stand-alone property. Second, the serial mechanism involves partial exclusion, which is important for the reduction of the free-rider problem. Received: June 10, 1996; revised version; February 11, 1997     

Generalized assignment models: with an applicationto technology transfer

Summary.  We consider a generalized assignment model where the payoffs depend on the number of matchings that take place. We formulate a simple non-cooperative game and look for subgame perfect equilibrium of this model. Existence is established for a wide class of games. We also look at a refinement criterion which, for the standard assignment model, selects the -optimal outcome as the unique equilibrium. We then apply these concepts to a model of technology transfer between domestic and foreign firms. Received: June 24, 1994; revised version October 12, 1995     

Condorcet cycles in bipartite populations

Summary. Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains. Received: June 17, 1996; revised version: April 15, 1997     

Quasitransitive social preference: why some very large coalitions have very little power

Summary. If only the strict part of social preference is required to be transitive then Independence of Irrelevant Alternatives implies that there is a coalition containing all but one individual that cannot force x to be socially ranked above y for at least half of the pairs of alternatives (x,y). Received: August 29, 1996; revised version: March 24, 1997     

The least core, kernel and bargaining sets of large games

Summary. We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally, we show that the Aumann-Maschler and the Mas-Colell bargaining sets contain the set of all countably additive payoff measures in the prekernel. Received: June 6, 1996; revised version: March 1, 1997     

On the uniqueness of competitive equilibrium

Summary . The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974). Received: July 1, 1996; revised version October 7, 1996     

Matching and bargaining models of markets: approximating small markets by large markets

Summary. We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.Received: January 22, 1996; revised version: September 24, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Efficient delays in a stochastic model of bargaining

Summary. We consider a k-player sequential bargaining model in which both the cake size and the identity of the proposer are determined by a stochastic process. For the case where the cake is a simplex (of random size) and the players share a common discount factor, we establish the existence of a unique stationary subgame perfect payoff which is efficient and characterize the conditions under which agreement is delayed. We also investigate how the equilibrium payoffs depend on the order in which the players move and on the correlation between the identity of the proposer and the cake size.Received: November 5, 1996; revised version: December 31, 1996This revised version was published online in February 2005 with corrections to the cover date.