Ori Haimanko

Strategic complements and substitutes, and potential games

Abstract 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. Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.

Voluntary Formation of Communities for the Provision of Public Projects

Abstract In this paper we examine a group formation problem, where heterogeneous individuals partitioned themselves into communities, each choosing its own public project from the given space of feasible projects. The model is that of “horizontal product differentiation” where individuals display distinct preferences over the policy space. We consider the notion of “efficient” configuration that minimizes the total project-related costs and aggregate personalized costs of all individuals, and “sustainable” configurations, those are immune against breakaways by subgroups of individuals. Our main result is that, with a unidimensional project space and single-peaked personalized costs, every efficient partition is sustainable.

On the existence of Bayesian Cournot equilibrium

We show that even in very simple oligopolies with differential information a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. However, we find sufficient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries. More general results arise when negative prices are allowed.

Partially Symmetric Values

We consider spaces of differentiable nonatomic and mixed vector measure games,pNA andpM, with finitely or countably many types of players. Type-symmetric values on these spaces of games are investigated (all Aumann and Shapley conditions except symmetry are assumed, the latter being replaced by a weaker assumption of covariance under automorphisms of the space of players that preserve each type). We show that if the types are uncountable, then type-symmetric values are random path values. In particular, the symmetric values onpM are characterized as mixtures of values defined in Hart (1973).

Compound voting and the Banzhaf index

Abstract We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition : the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index.

Optimal Scrutiny in Multi-Period Promotion Tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their respective skills, and intends to promote one of them at the end. In each period the agents choose effort levels and produce random outputs, independently of each other, and are fully informed of the past history of outputs. The principals major objective is to maximize the total expected output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and awards the promotion to the agent who produces more on the sample. This determines an extensive form game Gamma (T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if eta(T) is the maximal optimal sample size, then eta(T)/T approaches 0 as T approaches infinity.

Dominant strategies, superior information, and winner's curse in second-price auctions

Abstract. In a general model of common-value second-price auctions with differential information, we show equivalence between the following characteristics of a bidder: (i) having a dominant strategy; (ii) possessing superior information; (iii) being immune from winners curse. When a dominant strategy exists, it is given by the conditional expectation of the common value with respect to bidders information field; if the dominant strategy is used, other bidders cannot make a profit.

Dominance solvability of second-price auctions with differential information

We study a class of common-value second-price auctions with differential information. This class of common-value auctions is characterized by the property that each players information set is connected with respect to the common value. We showthat the entire class is dominance solvable, and that there is a natural single-valued selection from the resulting set of sophisticated equilibria. Additionally, it is shown that bidders information advantage over others is rewarded in sophisticated equilibria.

Cost sharing: the nondifferentiable case

We show existence and uniqueness of a cost allocation mechanism, satisfying standard axioms, on two classes of cost functions with major nondifferentiabilities. The first class consists of convex functions which exhibit nondecreasing marginal casts to scale, and the second of piecewise linear functions

Characterization of the Shapley-Shubik Power Index Without the Efficiency Axiom

We show that the Shapley-Shubik power index on the domain of simple (voting) games can be uniquely characterized without the e¢ ciency axiom. In our axiomatization, the e¢ ciency is replaced by the following weaker requirement that we term the gain-loss axiom: any gain in power by a player implies a loss for someone else (the axiom does not specify the extent of the loss). The rest of our axioms are standard: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, and dummy.