On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

A Suggested Interpretation of Some Experimental Results on Preplay Communication

M. Rabin (1994, J. Econ. Theory63, 370-391) proposes a model of behavior in two-person complete-information games with preplay communication, using non-equilibrium notions in the spirit of rationalizability to derive lower bounds on players' expected payoffs when players have unlimited communication opportunities. This paper adapts Rabin's model so that it can be used to analyze the results of the experiments of R. Cooper et al. (1989, Rand J. Econ.20, 568-587) on structured preplay communication in the Battle of the Sexes and the results of the unstructured bargaining experiments of Roth, Malouf, and Murnighan. Adding empirically motivated restrictions that allow the model to predict the payoff effects of changes in bounded communication possibilities like those in the experiments, it is shown that the data from both experiments are generally consistent with Rabin's model, and with the predictions of the extended model. Journal of Economic Literature Classification Numbers: C70, C72, C78, C91.     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

On Fixed-Path Rationing Methods

Moulin (J. Econ. Theory84 (1999), 41-72) characterizes the fixed-path rationing methods by efficiency, strategy-proofness, consistency, and resource-monotonicity. In this note we give a straightforward proof of his result. Journal of Economics Literature Classification Numbers: D63, D70.     

Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach

In this paper we propose a unifying approach to the study of optimal growth models with bounded or unbounded returns (above-below). Following our approach, we prove the existence of optimal solutions and show, without using the contraction method, that the value function is the unique solution to the Bellman equation for a particular class of functions. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. Moreover, following our approach we obtain the recent results of F. Alvarez and N. Stokey (1998, J. Econ. Theory82, 167-189) as well as the well-known results. Journal of Economic Literature Classification numbers: C61, 041.     

Subjective Uncertainty over Behavior Strategies: A Correction

In order to model the subjective uncertainty of a player over the behavior strategies of an opponent, one must consider the player's beliefs about the opponent's play at information sets that the player thinks have probability zero. This corregendum uses “trembles” to provide a definition of the convex hull of a set of behavior strategies. This corrects a definition we gave in [E. Dekel, D. Fudenberg, and D. K. Levine, 1999, J. Econ. Theory89, 165-185], which led to two of the solution concepts we defined there not having the properties we intended. Journal of Economic Literature Classification Numbers: C72, D82, C610.     

On the informational efficiency of the competitive resource allocation process

The purpose of this paper is to formalize the competitive process as a parametric process, and then prove the minimality of its message space among the message spaces for a broad class of parametric processes that includes the class of processes considered by Hurwicz (in “Studies in Resource Allocation Processes” (K. J. Arrow and L. Hurwicz, Eds.), pp. 413–423, Cambridge Univ. Press, Cambridge, 1977), Mount and Reiter (J. Econ. Theory6 (1974), 161–192), and Osana (J. Econ. Theory17 (1978), 66–78). The proof of this result turns crucially on the “asymmetry property” (which is stronger than the well-known “uniqueness property” of Hurwicz) and on an injectiveness lemma which is applicable to parametric processes.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

From private to public common agency

This note establishes that two propositions in the theory of private common agency by Laussel and Le Breton (J. Econ. Theory 100 (2001) 93) extend to a larger class of games, in which each principal's gross monetary payoff does not depend exclusively on the quantities she receives. A new result is offered to demonstrate that Proposition 4.3 is robust to the introduction of negative externalities. An existing result is reinterpreted to show that Proposition 4.2 is robust to the introduction of positive externalities.     

Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections

We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments, and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and as a special case, we obtain a long-standing claim to the same effect, due to R. McKelvey (Amer. J. Polit. Sci.30 (1986), 283-314), in the political science literature. Further, we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the coanalyticity and measurability of this set. In the concluding section, we indicate how the inclusion result may be extended to multiplayer, non-zero-sum games. Journal of Economic Literature Classification Numbers: C72, D72.     

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

The existence of competitive equilibrium in Laffont's (J. Econ. Theory10 (1975)) model of adverse selection with costly information is studied. The existence of an equilibrium with finite prices is demonstrated without unusual restrictions on preferences or the technology of information production. This is made possible by changing the way in which the behaviour of information producing agents is modelled, and allowing for some public information.     

Habit formation and long-run utility functions

This paper extends the work on habit formation of Pollak [Habit formation and dynamic demand functions. J. Polit. Econ. (1970)] and provides a critical counterexample to a conjecture of von Weizsäcker [Notes on endogenous changes of tastes, J. Econ. Theory (1971)] concerning the existence of a “long-run utility function.“ A linear specification of habit formation is applied to a general system of demand functions with linear Engel curves. It is shown that there exists a utility function which rationalizes the long-run demand functions if and only if they are the steady-state solution to a system of short-run demand functions generated by an additive utility function.     

Evolution in Games with Endogenous Mistake Probabilities

J. Bergin and B. Lipman (Econometrica64 (1996), 943-956) show that the selection effect from the random mutations in the adaptive population dynamics in M. Kandori, G. Mailath, and R. Rob (Econometrica61 (1993), 29-56) and P. Young (Econometrica61 (1993), 57-84) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some effort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). Journal of Economic Literature Classification Number: C72.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Coordination and transfer

We study the ability of subjects to transfer principles between related coordination games. Subjects play a class of order statistic coordination games closely related to the well-known minimum (or weak-link) and median games (Van Huyck et al. in Am Econ Rev 80:234–248, 1990, Q J Econ 106(3):885–910, 1991). When subjects play a random sequence of games with differing order statistics, play is less sensitive to the order statistic than when a fixed order statistic is used throughout. This is consistent with the prediction of a simple learning model with transfer. If subjects play a series of similar stag hunt games, play converges to the payoff dominant equilibrium when a convention emerges, replicating the main result of Rankin et al. (Games Econ Behav 32:315–337, 2000). When these subjects subsequently play a random sequence of order statistic games, play is shifted towards the payoff dominant equilibrium relative to subjects without previous experience. The data is consistent with subjects absorbing a general principle, play of the payoff dominant equilibrium, and applying it in a new related setting.     

Trembles in extensive games with ambiguity averse players

We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players’ preferences are represented by maxmin expected utility, as characterized in Gilboa and Schmeidler (J Math Econ 18(2):141–153, 1989), our definitions capture the intuition that players may consider the possibility of slight arbitrary mistakes. This generalizes the idea leading to trembling-hand perfect equilibrium as introduced in Selten (Int J Game Theory 4(1):25–55, 1975), by allowing for ambiguous trembles characterized by sets of distributions. We prove existence for two of our equilibrium notions and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to behavioral implications that are distinct from those attained under expected utility maximization, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.     

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

Are the treasures of game theory ambiguous?

Goeree and Holt (Am Econ Rev 91:1402?C1422, 2001) experimentally study a number of games. In each case, they initially find strong support for Nash equilibrium; however, by changing an apparently irrelevant parameter, they find results which contradict Nash equilibrium. In this paper, we study the five normal form games from Goeree and Holt (Am Econ Rev 91:1402?C1422, 2001). We argue that their results may be explained by the hypothesis that subjects view their opponents?? behaviour as ambiguous. Ambiguity-aversion causes players to avoid strategies, which give low out of equilibrium payoffs. Similarly, ambiguity preference can make strategies with high payoffs more attractive.     

Walras’ theory of capital formation: an intertemporal equilibrium reformulation

We develop a mainstream reformulation of the original Walras?? model of capital accumulation. We overcome the shortcomings of the original model. First, we prove the existence of intertemporal competitive equilibria. Our proof combines a well known theorem due to Yannelis and Prabhakar (J Math Econ 12:233?C245, 1983) with a lemma due to Geanakoplos (Econ Theory 21:585?C603, 2003). Secondly, we remedy the indeterminacy of allocation of savings across multiple types of capital goods by introducing a storage technology. Finally, we show that, for stored capital goods, the equality of rates of returns emerges endogenously in equilibrium, while it was imposed by Walras from the outset in his original contribution.