Marginal Subsidies in Tullock Contests

In a general Tullock contest, we examine a situation where a limited resource can be used to provide marginal subsidies to either player (weak or strong), or to increase the prize directly. We show that to maximize total effort, subsidizing the weak/strong player is preferred when the contest is sufficiently accurate/inaccurate. This result generalizes to n‐player lottery contests. In a lottery contest (Tullock contest with ), we derive the optimal scheme for a full range of resource: when the resource is small, it is optimal to only subsidize the weak player; when it is large, both players should be subsidized simultaneously.     

A general impossibility result on strategy-proof social choice hyperfunctions

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D^λ of lexicographic orderings which exhibits an impossibility of the Gibbard–Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D^λ. As most of the standard extension axioms induce superdomains of D^λ while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.     

Multi-unit auctions with budget limits

We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubel?s “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.     

Matching soulmates

We study iterated matching of soulmates (IMS), a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi, and Sönmez, except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions—that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In the Appendix we relate IMS to other well-known coalition formation processes.     

Fault Tolerant Implementation

In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most  k  faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties—  k  -monotonicity and no veto power—can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than     . As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.     

Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods

Public good economies where agents are endowed with strictly convex continuous single-peaked preferences on a convex subset of Euclidean space are considered. Such an economy arises for instance in the classical problem of allocating a given budget to finance the provision of several public goods where the agents have monotonically increasing strictly convex continuous preferences. A probabilistic mechanism assigns a probability distribution over the feasible alternatives to any profile of reported preferences. The main result of the paper establishes that any strategy-proof (in the sense of A. Gibbard, Econometrica45 (1977), 665-681) and unanimous mechanism must be a random dictatorship. Journal of Economic Literature Classification Numbers: D70, D71, H40, C60.     

A unifying impossibility theorem

This paper identifies and illuminates a common impossibility principle underlying a number of impossibility theorems in social choice. We consider social choice correspondences assigning a choice set to each non-empty subset of social alternatives. Three simple axioms are imposed as follows: unanimity, independence of preferences over infeasible alternatives, and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our axioms is serially dictatorial. A number of known impossibility theorems—including Arrow’s Impossibility Theorem, the Muller–Satterthwaite Theorem, and the impossibility theorem under strategic candidacy—follow as corollaries.     

Contests with a stochastic number of players

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.     

Cooperative Outcomes through Noncooperative Games

This paper shows the equivalence between the stable solution set of any cooperative game in characteristic form (G1) and the subgame perfect Nash equilibria in pure strategies of a certain noncooperative game (G2). Players of G1 are named "agents." G2 is played by different players ("principals") who compete in wages to attract agents. The equivalence result holds when there are enough principals (if the game is superadditive, two principals suffice). Finally, another related cooperative game (G3) is constructed with both principals and agents as players. For G2 and G3 the same result is then proven, for any number of principals. Journal of Economic Literature Classification Numbers: C71 and C72.     

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategyproof, anonymous and neutral.We reach an impossibility if, in addition, each agent's utility is at least , where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.     

Collusive dominant-strategy truthfulness

We show that collusion and wrong beliefs may cause a dramatic efficiency loss in the Vickrey mechanism for auctioning a single good in limited supply. We thus put forward a new mechanism guaranteeing efficiency in a very adversarial collusion model, where the players can partition themselves into arbitrarily many coalitions, exchange money with each other, and perfectly coordinate their actions. Our mechanism bypasses classic impossibility results (such as those of Green and Laffont, and of Schummer) by providing the players with a richer set of strategies, making it dominant for every coalition C to instruct each of its members to report truthfully not only his own valuation, but also his belonging to C. Our mechanism is coalitionally rational, which implies being individually rational for independent players.     

The Limitations of Experimental Design: A Case Study Involving Monetary Incentive Effects in Laboratory Markets

We replicate an influential study of monetary incentive effects by Jamal and Sunder (1991) to illustrate the difficulties of drawing causal inferences from a treatment manipulation when other features of the experimental design vary simultaneously. We first show that the Jamal and Sunder (1991) conclusions hinge on one of their laboratory market sessions, conducted only within their fixed-pay condition, that is characterized by a thin market and asymmetric supply and demand curves. When we replicate this structure multiple times under both fixed pay and pay tied to performance, our findings do not support Jamal and Sunders (1991) conclusion about the incremental effects of performance-based compensation, suggesting that other features varied in that study likely account for their observed difference. Our ceteris paribus replication leaves us unable to offer any generalized conclusions about the effects of monetary incentives in other market structures, but the broader point is to illustrate that experimental designs that attempt to generalize effects by varying multiple features simultaneously can jeopardize the ability to draw causal inferences about the primary treatment manipulation.     

On the strategic inconsistency of the meta-rights approach

Among many attempts to circumvent Sen's impossibility result Gibbard's theory of alienable rights has attracted attention of many researchers. Basu's (1984) theorem essentially depends on a Nash-type equilibrium concept. In this paper we introduce an alternative behavioral assumption where individuals have conjectures about the responses of others and investigate the robustness of Basu's result under this new solution concept. We also examine a possibility of coalition formation and cooperation under the meta-rights approach.For helpful discussions I would like to thank Rajat Deb, Joseph Greenberg, and Shlomo Weber. I am also indebted to an anonymous referee of this Journal for many valuable comments.     

Environmental Innovations and Firm Profitability: Unmasking the Porter Hypothesis

We examine impacts of different types of environmental innovations on firm profits. Following Porter’s (Sci Am 264(4):168, 1991) hypothesis that environmental regulation can improve firms’ competitiveness, we distinguish between regulation-induced and voluntary environmental innovations. We find that innovations which do not improve firms’ resource efficiency do not provide positive returns to profitability. However, innovations that increase a firm’s resource efficiency in terms of material or energy consumption per unit of output have a positive impact on profitability. This positive result holds for both regulation-induced and voluntary innovations, although the effect is greater for regulation-driven innovation. We conclude that the Porter hypothesis does not hold in general for its “strong” version, but depends on the type of environmental innovation. Our findings rest on firm-level data from the German part of the Community Innovation Survey 2008 (CIS 2008).     

GLOBAL GAMES WITH STRATEGIC SUBSTITUTES

We study global games with strategic substitutes. Specifically, for a class of binary‐action, ‐player games with strategic substitutes, we prove that under payoff asymmetry, as incomplete information vanishes, the global games approach selects a unique equilibrium. We characterize this equilibrium profile ; players employ switching strategies at different cutoff signals, the order of which is directly determined by payoff asymmetry. We provide examples that illustrate our result and its connection with dominance solvability. We extend the global game literature, which has thus far been developed for games with strategic complementarities, to new applications in industrial organization, collective action problems, finance, etc .     

Strategic market games with a finite horizon and incomplete markets

Summary. We study a strategic market game associated to an intertemporal economy with a finite horizon and incomplete markets. We demonstrate that generically, for any finite number of players, every sequentially strictly individually rational and default-free stream of allocations can be approximated by a full subgame-perfect equilibrium. As a consequence, imperfect competition may Pareto-dominate perfect competition when markets are incomplete. Moreover - and this contrasts with the main message conveyed by the market games literature - there exists a large open set of initial endowments for which full subgame-perfect equilibria do not converge to -efficient allocations when the number of players tends to infinity. Finally, strategic speculative bubbles may survive at full subgame-perfect equilibria.Received: 24 January 2002, Revised: 21 February 2003, JEL Classification Numbers: C72, D43, D52. Correspondence to: Gaël GiraudWe thank Tim Van Zandt for his comments.     

Repeated games with one-memory

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an ε-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.     

Emissions Trading with Updated Allocation: Effects on Entry/Exit and Distribution

Allocation of emissions allowances may have significant distributional and efficiency effects. It is well known that cost-efficiency may be achieved if allowances are auctioned or distributed in a lump sum manner, e.g., based on emissions levels before the start of the system (‘grandfathering’). Böhringer and Lange (Eur Econ Rev 49:2041–2055, 2005) show that a cost-effective outcome can also be achieved if the base year for allocation is continually updated (‘updating’), given that banking and borrowing are prohibited. In this paper we examine whether updating alters the entry and exit conditions for firms compared to grandfathering, and how it affects profits for new and existing firms. We find that the two schemes function surprisingly similar: First, the incentives to entry and exit are identical. Second, the total value of free quotas to existing firms, based on emissions before the system starts, is also identical without any auctioning. With updating initial claims for free allowances have a shorter lifetime compared to grandfathering, but quota prices are higher as firms anticipate the effect of current emissions on future claims to free allowances. The two effects exactly cancel each other out. If there is some combination of auction and free allocation, the total value of free quotas will always be highest under grandfathering if the auction rate is the same. Entry and exit incentives are still equal.