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ECON B " Game Theory. Guillermo Ordoñez. UCLA. February 1, 1 Bayesian games. So far we have been assuming that everything in the game was. Hence a Bayesian Nash equilibrium is a Nash equilibrium of the “expanded game” in which each player i's space of pure strategies is the set of maps from Θi to Si. Consider a finite incomplete information (Bayesian) game. Then a mixed strategy Bayesian Nash equilibrium exists. Video created by Stanford University, The University of British Columbia for the course "Game Theory". General definitions, ex ante/interim Bayesian Nash.


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The definition of Bayesian games has been combined with stochastic games to allow for environment states e.


Bayesian games specific example of a signaling game is a model of the job market. The players are the applicant agent and the employer principal. There are two types of applicant, skilled and unskilled.

Bayesian game

The employer's action space is the set of natural numbers, representing wages—these are used to form a contract based on how productive the applicant is expected to be.

Paying larger wages to skilled workers will generate larger payoffs for employers, while wages given to unskilled workers will have a less pronounced effect. The payoff of the employer is determined thus by the bayesian games of the applicant if the applicant accepts a contract and the wage paid.

Crucially, the employer chooses his or her action the wage offered according to his or her belief as to how skilled the applicant is and this belief is largely determined through signals sent by the applicant.

Bayesian game - Wikipedia

The applicant's action space consists bayesian games two actions: Obtaining an education is less costly for a skilled worker than for an unskilled worker, as a skilled worker may receive scholarships, find classes less taxing, and so on.

University education, therefore, serves as a signal, a means by which bayesian games applicant may communicate to the employer that he or she is, in fact, skilled.

Thus, it may be rational for an employer to prefer to employ university graduates, even if their studies are not related at all to the work they will do at the company.

One strategy the employer may use is to give all applicants a wage bayesian games that skilled applicants may attend university due to its lower cost but which is insufficient to provide university education for unskilled applicants. This creates a separating equilibrium: The employer can observe which workers can go to university, and can then maximize his or her payoff by providing high wages to skilled workers and low wages to unskilled.

Bayesian Nash equilibrium[ edit ] In a non-Bayesian game, a strategy profile is a Nash equilibrium if every strategy in that profile is a best response to every other strategy in the profile; i.

In a Bayesian game where players are modeled as risk-neutralrational players are seeking to maximize their expected payoff, given their beliefs about the other players in the bayesian games case, where players may be risk-averse or risk-loving, the assumption is that players are expected utility-maximizing.

A Bayesian Nash equilibrium is defined as a strategy profile and beliefs specified for each player about the types of the other players that maximizes the expected payoff for each player given their beliefs about the other players' types and given the strategies played by the other players.

This solution concept yields an abundance of equilibria in dynamic games when no further restrictions are placed on players' beliefs.

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This makes Bayesian Nash equilibrium an incomplete tool with which to analyze dynamic bayesian games of incomplete information. Perfect Bayesian equilibrium[ edit ] Main article: Perfect Bayesian equilibrium Bayesian Nash equilibrium results in some implausible equilibria in dynamic games, where players take turns sequentially rather than simultaneously.

Similarly, implausible equilibria might arise in the same way that implausible Nash equilibria arise in games of perfect and complete information, such as incredible threats and promises. Such equilibria might be eliminated in perfect and complete information games by applying subgame perfect Nash equilibrium.

However, it is not always possible to avail oneself of this solution concept in incomplete information games because such games contain non-singleton information sets and since bayesian games must contain complete information sets, sometimes there is only one subgame—the entire game—and so every Nash equilibrium is bayesian games subgame perfect.


Even if a game does have more than one subgame, the inability of subgame perfection to cut through information sets can result in implausible equilibria not being eliminated.

To refine the equilibria generated by the Bayesian Nash solution concept or subgame perfection, one can apply the Perfect Bayesian equilibrium solution concept. PBE is in the spirit of subgame perfection in that it demands that subsequent play be optimal.

However, bayesian games places player beliefs on decision nodes that enables moves in non-singleton information bayesian games to be dealt more satisfactorily.