Language, meaning and games A model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to two-sided preplay communication in finite and symmetric two-player games and we establish that, in generic and symmetric n × n - coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We extend the approach to one-sided communication in finite, not necessarily symmetric, two-player games.

Corporate Control and the Stock Market

This paper studies a general equilibrium model with an investor controlled firm. Shareholders can vote on the firm’s production plan in an assembly. Prior to that they may trade shares on the stock market. Since stock market trades determine the distribution of votes, trading is strategic. There is always an equilibrium, where share trades lead to owners deciding for competitive behavior, but there may also be equilibria, where monoplistic behavior prevails.Corporate governance, general equilibrium, objective function of the firm, shareholder voting, stock markets.

Language, meaning and games: a model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of two-sided pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to finite and symmetric two-player games and we establish that, in generic and symmetric n x n -coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We discus Aumann’s (1990) example of a Pareto efficient equilibrium that is not self-enforcing. We also extend the approach to one-sided communication.Communication, coordination, language, honesty, evolutionary stability.

Where strategic and evolutionary stability depart - a study of minimal diversity games

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.Strategic form games, strategic stability, evolutionary stability

Intergenerational equity and stationarity

We consider quasi-orderings of infinite utility streams satisfying the strong Pareto axiom (i.e., Paretian quasi-orderings) and study the question of how strong a notion of intergenerational equity one can impose on these quasi-orderings without generating an impossibility theorem. Building on a result by Mitra and Basu (2007), we first show that there exist many possible extensions of the finite anonymity axiom that are satisfied by some Paretian quasiordering. Then we study how the additional requirement of stationarity `a la Koopmans (1960) affects this result. After proving a possibility theorem for this case, we demonstrate that stationarityimposes strong restrictions on the extendability of the finite anonymity axiom.

The Simple Geometry of Perfect Information Games

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.Perfect information, Subgame perfection, Equilibrium correspondence

Some preliminary remarks on the relevance of topological essentiality in general equilibrium theory and game theory

We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement.fixed point theory, game theory, equilibrium theory, stability of Nash equilibrium, multiplicity of equilibria

Evolution towards efficient coordination in repeated games, preliminary version

We show that in long repeated games- or in infinitely repeated games with discount rate close to one- payoffs corresponding to evolutionary stable sets are asymptotically efficient, as intuition suggests. Actions played at the beginning of the game are used as messages that allow players to coordinate on Pareto optimal outcomes in the following stages. Strategies following some simple and intuitive "behavioral maxims" are shown to be able to drive out inefficient ones from a population. The result builds a bridge between the theory of repeated games and that of communication games that will be further investigated