Concept Of Bayesian Equilibrium Research Articles

Imperfect certification and eco-labelling of products

PurposeThis paper aims to investigate the role of certification in providing information and reducing market inefficiencies when the “certification process is imperfect”. In the setting, eco-labels imperfectly signal environmental product quality to consumers where the error in the process of certification could be either Type 1 or Type 2 error. The paper examines firms' incentive to get certified, equilibrium quantities and profits. The authors use perfect Bayesian equilibrium concept for the analysis. They then examine conditions for separating and pooling equilibrium to exist and welfare implications of certification process.Design/methodology/approachThe paper uses a vertical product differentiated model where firms are competing in quantities. Consumers are unable to observe the environmental quality of the product. To signal the product quality to consumers, firms may adopt certification by a third party. Using a framework where certification process is imperfect, the paper derives conditions for Perfect Bayesian separating and pooling equilibrium to exist.FindingsThe paper shows that the existence of separating and pooling equilibrium depends on the certification fee. A separating equilibrium, where one firm seeks certification and other firm does not seek certification exists for an intermediate value of certification fee. A pooling equilibrium, where both firms seek certification, exists only when the certification fee is sufficiently small. The paper shows conditions for the certification fee for which welfare will be higher under separating equilibrium as compared to pooling equilibrium and analyses welfare implications for subsidy policy for the certification fee.Originality/valueThe paper contributes to the literature by examining the role of labelling under imperfect certification.

The Penalty-Kick Game Under Incomplete Information

This paper presents a model of the penalty-kick game between a soccer goalkeeper and a kicker, in which there is uncertainty about the kicker’s type (and there are two possible types of kicker). To find a solution for this game we use the concept of Bayesian equilibrium, and we find that, typically, one of the kicker’s types will play a mixed strategy while the other type will choose a pure strategy (or, sometimes, a “restricted mixed strategy”). The model has a simpler version in which the players can only choose between two strategies (right and left), and a more complex version in which they can also choose a third strategy (the center of the goal). Comparing the incomplete-information Bayesian equilibria with the corresponding complete-information Nash equilibria, we find that in all cases the expected scoring probability increases (so that, on average, the goalkeeper is worse off under incomplete information). The three-strategy model is also useful to explain why it could be optimal for a goalkeeper never to choose the center of the goal (although at the same time there were some kickers who always chose to shoot to the center).

Playing against an Apparent Opponent: Incentives for Care, Litigation, and Damage Caps under Self-Serving Bias

This paper presents a strategic model of incentives for care and litigation under asymmetric information and self-serving bias, and studies the effects of damage caps. We contribute to the behavioral economics literature by generalizing the perfect Bayesian equilibrium concept to environments with biased litigants. Our main findings are as follows. First, our results suggest that self-serving bias might be welfare-reducing. The negative impact of this cognitive bias on social welfare is explained by the reduction in the level of care, and the increase in the likelihood of disputes. We also find that self-serving bias helps litigants commit to tough negotiation positions. However, it is economically self-defeating for the informed plaintiff. Second, our findings indicate that caps on non-economic damages might reduce the level of care. Importantly, we find that the positive effect of damage caps on lowering the likelihood of disputes, commonly attributed to caps, does not necessarily hold in environments with biased litigants: Caps might induce higher likelihood of disputes. Our findings are aligned with empirical and experimental evidence.

An Experimental Test of Career Concerns

Holmstrom's (1982/99) career concerns model has become an important workhorse for the analysis of agency issues in many fields. The underlying signal jamming argument requires players to use information in a Bayesian way - which may or may not reasonably approximate real-life decision makers' behavior. Testing this theory with field data is dicult since typically little is known about the information that individuals base their decisions on, and this explains the dearth of empirical studies. We provide experimental evidence that the signal jamming mechanism works in a laboratory setting. Moreover, subjects' beliefs fit remarkably well requirements imposed by the Bayesian equilibrium concept.

Joint Coherence in Games of Incomplete Information

Decisions are often made under conditions of uncertainty about the actions of supposedly-rational competitors. The modeling of optimal behavior under such conditions is the subject of noncooperative game theory, of which a cornerstone is Harsanyi's formulation of games of incomplete information. In an incomplete-information game, uncertainty may surround the attributes as well as the strategic intentions of opposing players. Harsanyi develops the concept of a Bayesian equilibrium, which is a Nash equilibrium of a game in which the players' reciprocal beliefs about each others' attributes are consistent with a common prior distribution, as though they had been jointly drawn at random from populations with commonly-known proportions of types. The relation of such game-theoretic solution concepts to subjective probability theory and nonstrategic decision analysis has been controversial, as reflected in critiques by Kadane and Larkey and responses from Harsanyi, Shubik, and others, which have appeared in this journal. This paper shows that the Bayesian equilibrium concept and common prior assumption can be reconciled with a subjective view of probability by (i) supposing that players elicit each others' probabilities and utilities through the acceptance of gambles, and (ii) invoking a multi-agent extension of de Finetti's axiom of coherence (no arbitrage opportunities, a.k.a. “Dutch books”). However, the Nash property of statistical independence between players is weakened, and the probability distributions characterizing a solution of the game admit novel interpretations.

Product availabilty as a strategic variable: The implications of regulating retailer stockouts

We study product availability as a strategic variable in a sequential game between consumers and a monopolist. We use a perfect Bayesian equilibrium concept to solve the game under different regulatory regimes. We show that under certain assumptions about the regulatory environment, a two-price equilibrium in which the quantity of the lower-priced good is limited may exist even when a single retailer sells two brands that are perfect substitutes. The FTC Guides Against Bait Advertising are shown to be potentially welfare enhancing as they facilitate commitment on the part of a monopolist credibly to plan for stockouts. Paradoxically, our analysis suggests that the more stringent FTC regulation prohibiting stockouts by retail food stores from 1971 to 1988 was Pareto worsening, as it removed the monopolist's commitment mechanism.

Correlated equilibria and the dynamics of rational deliberation

De Finetti and Ramsey showed how rational decision is founded on coherence. This should be true in game theoretic contexts just as much as in other ones. If followed to their logical conclusion considerations of coherence can lead to dynamic deliberation and in this context introduce a natural Bayesian equilibrium concept. Such deliberational equilibria are intimately connected with game theoretic equilibria in games played by Bayesian deliberators. In the simplest cases deliberation is trivial; one calculates expected utility and maximizes. But in more interesting cases, the very process of deliberation may generate information which is relevant to the evaluation of the expected utilities.2 Then, processing costs permit? ting, a Bayesian deliberator will feedback that information and recal? culate the expected utilities in light of the new knowledge.3 In such an interesting decision problem, deliberation can be modeled as a dynamic system. The decision maker starts in a state of indecision; calculates expected utility; moves in the direction of max? imum expected utility; feeds back the information generated and recalculates; etc. In this process, his probabilities of doing the various acts evolve until, at the time of decision, his probabilities of doing the selected act become virtually one. Dynamic deliberation carries with it an equilibrium principle for individual decision. The decision maker cannot decide to do an act