Games of incomplete information without common knowledge priors

We relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi’s type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium (BNE) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE.inconsistent beliefs, games of incomplete information, finite belief hierarchy

A meaningful two-person bargaining solution based on ordinal preferences

In this note I argue that the traditional argument proving the non-existence of two-person ordinal bargaining solutions is misleading, and also provide an example of such a solution.

Reference price distortion

I show that when consumers (mis)perceive prices relative to reference prices, budgets turn out to be soft, prices tend to be lower and the average quality of goods sold decreases. These observations provide explanations for decentralized purchase decisions, for people being happy with a purchase even when they have paid their “valuation”, and for why trade might be detrimental to welfare.

Revenue sharing in professional sports leagues: for the sake of competitive balance or as a result of monopsony power?

We analyze the distribution of broadcasting revenues by sports leagues. In the context of an isolated league, we show that when the teams engage in competitive bidding to attract talent, the league's optimal choice is full revenue sharing (resulting in full competitive balance) even if the revenues are independent of the level of balancedness. This result is overturned when the league has no monopsony power in the talent market. When the teams of two different leagues bid for talent, the equilibrium level of revenue sharing is bounded away from sharing of revenues: leagues choose a performance-based reward scheme. Finally, we argue that our model explains the observed differences in revenue sharing rules used by the U.S. sports leagues (full revenue sharing) and European soccer leagues (performance-based reward).

Delegated Bargaining and Renegotiation

We examine the commitment effect of delegated bargaining when the delegation contract is renegotiable. We consider a seller who can either bargain face-to-face with a prospective buyer or delegate bargaining to an intermediary. The intermediary is able to interrupt negotiating with the buyer to renegotiate the delegation contract. We show that the time cost of renegotiation prevents a full elination of the commitment effect of delegation. Indeed, there are always gains from delegation when the players are sufficiently patient. An extension to search market environment shows that the gains from delegation are negatively related to the efficiency of search.bargaining, commitment, delegation, renegotiation, search

Speculating against an overconfident market

We distinguish two components of self-confidence in a financial market: private confidence measures the self-confidence level of speculators, while public confidence measures the confidence level they attribute to their competitors. We then study how independent changes in these components affect the equilibrium trading strategies. We conduct the analysis in a financial market with imperfect competition where investors submit limit orders. We calculate the unique linear symmetric equilibrium as well as the major indicators of the market. In addition to providing a partial explanation for the excess volatility of asset prices as well as for trading volume unexplained by the arrival of new information, our model highlights the differences between the effects of public versus private confidence.overconfidence, financial markets, imperfect competition

Inter-league competition for talent vs. competitive balance

We analyze the distribution of broadcasting revenues by sports leagues. We show that when the teams engage in competitive bidding to attract talent in an isolated league, the league’s optimal choice is full revenue sharing (resulting in full competitive balance). In contrast, when the teams of several leagues bid for talent, in equilibrium the leagues choose a performance-based reward scheme. We thus provide an explanation for the differences in revenue sharing rules for national TV rights used by the U.S. sports leagues (full revenue sharing) and European football leagues (performance-based reward).Sports league, revenue sharing, competitive balance.

Olson vs. Coase: coalitional worth in conflict

We analyze a model of conflict with endogenous choice of effort, where subsets of the contenders may force the resolution to be sequential: First the alliance fights it out with the rest and – in case they win – later they fight it out among themselves. For three-player games, we find that it will not be in the interest of any two of them to form an alliance. We obtain this result under two different scenarios: equidistant preferences with varying relative strengths, and vicinity of preferences with equal distribution of power. We conclude that the commonly made assumption of super-additive coalitional worth is suspect.coalition formation, conflict, alliance.