The Logic of Joint Ability in Two-Player Tacit Games

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality

Coalition-Stable Equilibria in Repeated Games

It is well-known that subgame-perfect Nash equilibrium does not eliminate incentives for joint-deviations or renegotiations. This paper presents a systematic framework for studying non-cooperative games with group incentives, and offers a notion of equilibrium that refines the Nash theory in a natural way and answers to most questions raised in the renegotiation-proof and coalition-proof literature. Intuitively, I require that an equilibrium should not prescribe in any subgame a course of action that some coalition of players would jointly wish to deviate, given the restriction that every deviation must itself be self-enforcing and hence invulnerable to further self-enforcing deviations. The main result of this paper is that much of the strategic complexity introduced by joint-deviations and renegotiations is redundant, and in infinitely-repeated games with discounting every equilibrium outcome can be supported by a stationary set of optimal penal codes as in Abreu (1988). In addition, I prove existence of equilibrium both in stage games and in repeated games, and provide an iterative procedure for computing the unique equilibrium-payoff setCoalition, Renegotiation, Game Theory

Choosing and Sharing

Choosing a project for which benefits accrue to all involved agents but brings major costs or additional benefits to only one agent is often problematic. Siting a nationwide nuclear waste disposal or hosting a major sporting event are examples of such a problem: costs or benefits are tied to the identity of the host of the project. Our goals are twofold: to choose the efficient site (the host with the lowest cost or the highest localized surplus) and to share the cost, or surplus, in a predetermined way so as to achieve redistributive goals. We propose a simple mechanism to implement both objectives. The unique subgame-perfect Nash equilibrium of our mechanism coincides with truthtelling, is efficient, budget-balanced and immune to coalitional deviations.

Mechanisms in the Core of a Fee Game

A Fee Game is a cooperative game with incomplete information the ex post realizations of which show side payment character. The game appears in coalitional function form depending on the 'types' of the players which are randomly chosen and about which the players have private information. We specify incentive compatible mechanisms and show that with a natural condition the core of the game is not empty: it contains constant mechanisms.

Rivalry, Exclusion and Coalitions

Coalition formation, exclusion contest, tragedy of the commons

Network Markets and Consumer Coordination

This paper analyzes pricing decisions and competition in network markets, assuming that groups of consumers can coordinate their choices when it is in their interest, if coordination does not require communication. It is shown that multiple asymmetric networks can coexist in equilibrium. A monopolist might operate multiple ex ante identical networks to price differentiate. In Bertrand competition different firms might target high reservation value consumers on different sides of the market. Firms can obtain positive profits in price competition. Product differentiation in equilibrium is endogenized by consumers' network choices. Enough heterogeneity in reservation values is necessary for existence of these asymmetric equilibria.two-sided markets, network externalities, platform competition, coordination

Endogenous Coalition Formation in Contests

This paper analyzes coalition formation in a model of contests with linear costs. Agents first form groups and then compete by investing resources. Coalitions fight for prizes that are assumed to be subject to rivalry, so their value is non-increasing in the size of the group. This formulation encompasses as particular cases some models proposed in the rent-seeking literature. We show that the formation of groups generates positive spillovers and analyze two classes of games of coalition formation. A contest among individual agents is the only stable outcome when individual defections leave the rest of the group intact. More concentrated coalition structures, including the grand coalition, are stable when groups collapse after a defection, provided that rivalry is not too strong. Results in a sequential game of coalition formation suggest that there exists a non-monotonic relationship between the level of underlying rivalry and the level of social conflict.Contests, coalition formation, conflict, rivalry.

Choosing and Sharing

Implementing a project, like a nationwide nuclear waste disposal, which benefits all involved agents but brings major costs only to the host is often problematic. In practice, revelation issues and redistributional concerns are significant obstacles to achieving stable agreements. We address these issues by proposing the first mechanism to implement the efficient site (the host with the lowest cost) and share the exact cost while retaining total control over realized transfers. Our mechanism is simple and in the vein of the well-known Divide and Choose procedure. The unique Nash equilibrium outcome of our mechanism coincides with truthtelling, is budget-balanced, individually rational and immune to coalitional deviations. More generally, our mechanism can also handle the symmetric case of positive local externalities (e.g., Olympic Games) and even more complex situations where the usefulness of the project---regardless of its location---is not unanimous.Public goods; local externalities; NIMBY; implementation; mechanism design; VCG mechanisms

Collectively Incentive Compatible Tax Systems

This paper assumes that individuals possess private information both about their abilities and about their valuation of a public good. Individuals can undertake collective actions on order to manipulate the tax system and the decision on public good provision. Consequently, an implementable scheme of taxation has to be collectively incentive compatible. If preferences are additively separable, then an implementable tax systems has the following properties: (i) tax payments do not depend on public goods preferences and (ii) there is no scope for a collective manipulation of public goods preferences. For a quasilinear economy, the optimal tax system is explicitly characterized.Optimal Taxation, Public Good Provision, Revelation of Preferences, Information Aggregation