This paper presents a dynamic model in which agents adjust their decisions in the direction of higher payoffs, subject to random error. This process produces a probability distribution of players’ decisions whose evolution over time is determined by the Fokker-Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studie...

We show that under horizontal differentiation pure symmetric Cournot equilibria exist if firms react to a rise in competitors’ output in such a way that their market price does not rise. This condition is related to strategic complementarity, but not to convexity or differentiability. We rule out multiple equilibria under some additional conditions and discuss stability and regularity of equili...

New relaxations of the Nash equilibrium concept are shown to exist in any strategic game with discontinuous payoff functions. The new concepts are used (1) to show the equivalence between Reny’s better-reply security condition [28] and Simon-Zame’s endogenous tie-breaking rule equilibrium concept [32], (2) to obtain conditions for the existence of approximated equilibria in a class of discontin...

This paper develops an endogenous growth model of a dual economy where human capital accumulation is the source of economic growth. The dualism between the rich individuals and the poor individuals exists in the mechanism of human capital accumulation. Rich individuals allocate labour time not only for their own production and knowledge accumulation but also to train the poor individuals. Stead...

We study how asymmetric information affects the set of rationalizable solutions in a linear setup where the outcome is determined by forecasts about this same outcome. The unique rational expectations equilibrium is also the unique rationalizable solution when the sensitivity of the outcome to agents’ forecasts is less than one, provided that this sensitivity is common knowledge. Relaxing this ...

Let G be an N -player game in strategic form and C be a set of permissible coalition of players (exogenously given). A strategy profile σ is a coalitional-equilibrium if no permissible coalition in C has a unilateral deviation that profits to all its members. At the two extremes: when C contains only singleton players, σ reduces to a Nash equilibrium and when C consists on all coalitions of pla...

I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some qualifications, games with a unique equilibrium have complementarities if and only if Cournot bestresponse dynamics has no cycles; and that all games with multiple equilibria have complementarities. As applications of my results, I show: 1. That generic 2X2 ...

I prove that, in models with complementarities, some non-monotone comparative statics must select unstable equilibria; and, under additional regularity conditions, that monotone comparative statics selects stable equilibria. JEL Classification. C61, C62, C72, C73. Discussions with my advisers, Ilya Segal and Chris Shannon, were very important for this work. I am very grateful for their help. I ...

In this paper, we consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other. In such a game, we adopt the party-unanimity Nash equilibrium (PUNE) [Roemer (1998; 1999; 2001)] as an appropriate solution concept, and examine the general existence problem of th...

Stable networks of order  where  is a natural number refer to those networks that are immune to coalitional deviation of size  or less. In this paper, we introduce stability of a finite order and examine its relation with efficient networks under anonymous and component additive value functions and the component-wise egalitarian allocation rule. In particular, we examine shapes of networks o...