Strategic Substitutes and Potential Games

We show that games of strategic substitutes (or complements) with aggregation are "pseudo-potential" games, and therefore possess Nash equilibria in pure strategies. Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.

Decision rules revealing commonly known events

We provide a sufficient condition under which an uninformed principal can infer any information that is common knowledge among two experts, regardless of the structure of the parties’ beliefs. The condition requires that the bias of each expert is less than the radius of the smallest ball containing the action space

Optimal fees in internet auctions

An auction house runs a second-price auction with a possibility of resale through re-auctions. It collects listing and closing fees from the seller. We find the fees which maximize the revenue of the auction house. In particular, we show that the optimal listing fee is zero. Our findings are consistent with the policies of eBay, Amazon, Yahoo, and other Internet auctions

Bargaining with a property rights owner

We consider a bargaining problem where one of the players, the intellectual property rights owner (IPRO) can allocate licenses for the use of this property among the interested parties (agents). The agents negotiate with him the allocation of licenses and the payments of the licensees to the IPRO. We state five axioms and characterize the bargaining solutions which satisfy these axioms. In a solution every agent obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are the same across all agents and all bargaining problems. The IPRO obtains the remaining surplus. The symmetric solution is the nucleolus of a naturally related coalitional game.</p

Strategic complements and substitutes, and potential games

&lt;p&gt;We show that games of strategic complements, or substitutes, with aggregation are “pseudo-potential” games. The upshot is that they possess Nash equilibria in pure strategies (NE), even if the strategy sets are not convex; and that various dynamic processes converge to NE. In particular, NE exist in Cournot oligopoly with indivisibilities in production.&lt;/p&gt; &lt;p&gt;Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.&lt;/p&gt