Plenary Lecture
Pareto Optimum in Bayesian Games
Professor Mihai Daniel Roman
The Faculty of Cybernetics
Statistics and Economic Informatics
The Bucharest University of Economic Studies
Romania
E-mail: mihai.roman@ase.ro
Abstract: The solutions provided by Game Theory are usually specific for different types of games and start from Nash solutions. The Nash equilibrium is specific for non cooperative static games in complete information, Perfect Subgame Equilibrium corresponds to non cooperative sequential games in complete and perfect information, Bayes-Nash equilibrium is specific for static non cooperative games in incomplete information and Perfect Bayes-Nash equilibrium for dynamic non cooperative games in incomplete information. A Nash equilibrium (or different forms of them) basically represents a set of strategies where each player tries to maximize his or her payoff depending on their own strategies and given the possible strategies of the others. Usually, there are not exists a direct relation between Nash equilibrium and Pareto optimal solutions (defining Pareto optimal solution as the state where it is not possible to improve the one player payoff without making the other players’ payoff worse). One of the most important examples of this situation is Prisoner Dilemma, where Nash equilibrium is not Pareto optimal. But it is well known that every game has at least one Pareto optimal profile that is not necessary a Nash equilibrium). In the case of non cooperative static game in complete information there are a few games categories (like coordination games) where it is possible to implement Pareto optimum solutions as Nash equilibriums. The case of non cooperative games in complete and perfect information confirms the possibility to obtain Perfect Subgame Equilibrium outside Pareto optimal solutions. One particular situation is in the case of repeated (finite or infinite) games where it is possible to obtain both Pareto optimum and Perfect Subgame Equilibrium for the same set of strategies (under conditions established in folk theorem). Also the Perfect Bayes Nash Equilibriums that corresponds to dynamic non cooperative games in incomplete information usually do not correspond to Pareto optimum without specific constraints. Moreover, in the case of dynamic mechanism design games, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayes - Nash equilibrium of an extensive form game. The correspondence between Bayes-Nash equilibrium and Pareto optimum for static non cooperative games in incomplete information was less studied in literature. In our study we analyze different types of Bayesian games (like mechanism design games, moral hazard games, adverse selection games or auction games) and we verify the relation between Bayes –Nash equilibrium and Pareto optimum. The main result was that under incomplete information it is not possible to implement the Pareto optimum (or the first best optimum) simultaneously with Bayes – Nash equilibrium (that usually was the second best optimum).
Brief Biography of the Speaker: Mihai Daniel Roman is a full professor of Game Theory and Macroeconomics at The Faculty of Cybernetics, Statistics and Economic Informatics, The Bucharest University of Economic Studies, Romania. He received his master degree in 1994 at the Université de Sciences Sociales, Toulouse, France, specialization Quantitative Economics and the Ph. D. in 1997 at The Bucharest University of Economic Studies in the field of Economic Cybernetics. His scientific interests are primarily focused on Game Theory, Macroeconomics and Quantitative Economic Analysis. As a director, he has conducted more than twenty national research projects, he published more than thirty papers in international prestigious journals, he presented more than one hundred and twenty papers at international and national conferences and he wrote twenty four books. He is a member of the editorial board in six database indexed international journals. He is also the director of the Advanced Research Center for Microeconomic and Macroeconomic Cybernetic Analysis and he organized eight international conferences in the field of economic cybernetic analysis. Since 2012 he has been elected the Vice-president of The Bucharest University of Economic Studies Senate.