Renegotiations in the Greenhouse

International climate policies are being shaped in a process of ongoing negotiations. This paper develops a sequential game framework to explore the stability of international climate agreements allowing for multiple renegotiations. We analyse how the incentives to reach an international climate agreement in the first period will be impacted by the prospect of further negotiations in later periods and by the punishment options related to renegotiations. For this purpose we introduce a dynamic model of coalition formation with twelve world regions that captures the key features of the climate-economy impacts of greenhouse gas emissions. For a model with one round of renegotiations we find that a coalition of China and the United States is the unique renegotiation proof equilibrium. In a game with more frequent renegotiations we find that the possibility to punish defecting players helps to stabilise larger coalitions in early stages of the game. Consequently, several renegotiation proof equilibria emerge that outperform the coalition of China and USA in terms of abatement levels and global payoff. The Grand Coalition, however, is unstable.     

Tax Rate Harmonization,Renegotiation, and Asymmetric Tax Competition for Profits with Repeated Interaction

This paper analyzes a model of corporate tax competition with repeated interaction and with strategic use of profit shifting within multinationals. We show that international tax coordination is more likely to prevail if the degree of asymmetry in terms of productivity differences between countries is smaller, or if concealment costs of profit shifting are larger when the tax authorities adopt grim‐trigger strategies. Allowing for renegotiation in the tax harmonization process requires more patient tax authorities to implement tax harmonization as a weakly renegotiation‐proof equilibrium. In this case, we find somewhat paradoxical situations where higher costs of profit shifting make tax harmonization less sustainable.     

FINITELY REPEATED PRISONERS' DILEMMA WITH SMALL FINES: THE PENANCE CONTRACT*

This paper investigates finitely repeated prisoners' dilemma games with explicit contractual devices. It shows that full collusion can be achieved in a unique manner by incentivizing the players' final‐period play with small fines. The incentivizing modality is the penance contract, by which a player is penalized if and only if he deviates from the penance strategy in the final period. Using this contractual agreement brings the penance strategy profile into unique subgame perfect equilibrium in the entire game and achieves full collusion without being invalidated by renegotiation.     

Dynamic common agency

A general model of dynamic common agency with symmetric information is considered. The set of truthful Markov perfect equilibrium payoffs is characterized and the efficiency properties of the equilibria are established. A condition for the uniqueness of equilibrium payoffs is derived for the static and the dynamic game. The payoff is unique if and only if the payoff of each principal coincides with his marginal contribution to the social value of the game. The dynamic model is applied to a game of agenda setting.     

Enjoy the silence: an experiment on truth-telling

We analyze experimentally two sender–receiver games with conflictive preferences. In the first game, the sender can choose to tell the truth, to lie, or to remain silent. The latter strategy is costly. In the second game, the receiver must decide additionally whether or not to costly punish the sender after having observed the history of the game. We investigate the existence of two kinds of social preferences: lying aversion and preference for truth-telling. In the first game, senders tell the truth more often than predicted by the sequential equilibrium analysis, they remain silent frequently, and there exists a positive correlation between the probability of being truthful and the probability of remaining silent. Our main experimental result for the extended game shows that those subjects who punish the sender with a high probability after being deceived are precisely those who send fewer but more truthful messages. Finally, we solve for the Perfect Bayesian Nash Equilibria of a reduced form of the baseline game with two types of senders. The equilibrium predictions obtained suggest that the observed excessive truth-telling in the baseline game can be explained by lying aversion but not by a preference for truth-telling.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users. Financial support through the Ramón y Cajal program of the Spanish Ministry of Education and Science is gratefully acknowledged. This work was initiated while the author was working at Maastricht University.     

Rent Seeking and Allocative Efficiency

This paper considers a rent‐seeking game (specifically, a winner‐takes‐all contest) with incomplete information. By allowing for sequential moves, a Bayesian‐Stackelberg equilibrium can be constructed. It can be shown that, at the Bayesian‐Stackelberg equilibrium, it is always possible that the allocative efficiency argument fails. That is, there are cases in which the Stackelberg follower is more efficient but loses the contest. Using a specific class of distributions, it is also shown that sometimes the corrupt official will choose the Bayesian‐Stackelberg equilibrium over the Bayesian‐Nash equilibrium in order to maximise the expected bribe revenue. That is, when designing the rules of the rent‐seeking game, the dynamic nature of competition will be taken into account.     

Forming Efficient Free‐Trade Networks: A Sequential Mechanism

This paper considers a sequential network formation game, whose subgame‐perfect equilibrium can generate an efficient and complete network as the equilibrium outcome, thereby achieving global free trade. Our result shows that bilateral free‐trade agreements can be compatible with global free trade.     

Selecting equilibria in common agency games

We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices.As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information.     

Information transmission and inefficient lobbying

In a seminal paper, Grossman and Helpman (1994) introduced a framework to understand how lobbying influences the choice of import/export tariffs. In this paper we extend their analysis and assume that lobbies have private information to analyze the effects of information transmission in a Grossman and Helpman lobby game. Information transmission leads to two agency costs. One refers to the cost of signaling and the other to the cost of screening the lobby's competitiveness. The signaling cost reduces distortions resulting from the screening cost. On the other hand, distortions from the screening cost enhance the signaling cost. The two combined effects generate more distortions in the political game than each effect separately. Tariff protection and lobbies' rents are lower than those found in Grossman and Helpman's truthful equilibrium. Therefore, information transmission may improve welfare through the reduction of rent-seeking activities.     

Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

SCREENING AS A UNIFIED THEORY OF DELINQUENCY,RENEGOTIATION, AND BANKRUPTCY

We propose a parsimonious model with adverse selection where delinquency, renegotiation, and bankruptcy all occur in equilibrium as a result of a simple screening mechanism. A borrower has private information about her endowment, and a lender uses random contracts to screen different types of borrowers. In equilibrium, some borrowers choose not to repay and thus become delinquent. The lender renegotiates with some delinquent borrowers. In the absence of renegotiation, delinquency leads to bankruptcy. Applied to mortgage restructuring, our mechanism generates amplification of house‐price shocks through foreclosure spillovers. We also show that government intervention aimed at limiting foreclosures may have unintended consequences.     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

Perturbed communication games with honest senders and naive receivers

This paper studies communication games in which the sender is possibly honest (tells the truth) and the receiver is possibly naive (follows messages as if truthful). The characterization of message-monotone equilibria in the perturbed games explain several important aspects of strategic communication including sender exaggeration, receiver skepticism and message clustering. Surprisingly, the strategic receiver may respond to more aggressive claims with more moderate actions. In the limit as the probabilities of the non-strategic players approach zero, (i) the limit equilibrium corresponds to a most-informative equilibrium of the limit (Crawford-Sobel) game; (ii) only the top messages are sent.     

Voluntary Contributions to Multiple Public Projects

The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game , is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be a generalized ordinal potential game ; a best–response in the contribution game implies a best response in a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corresponds in a natural way with a core element of the realization game, and vice versa. Moreover, each strong Nash equilibrium is coalitional proof.     

产业技术创新联盟知识共享的两阶段博弈分析

为推动产业技术创新联盟知识共享的高效率均衡,综合考虑知识的经济特征和产业导向的准公共性,设计了基于自组织和他组织知识共享的两阶段博弈模式。第一阶段,构建基于位势和效用的知识共享博弈模型,对比分析联盟集中决策与分散决策下成员个体特征、联盟特征等因素对知识共享效用的影响机理;第二阶段,建立基于激励和效用的知识共享博弈模型,剖析个体特征、联盟特征、联盟激励对知识共享效用的影响机理,并结合数值算例进行验证。由此,构建“自组织+他组织”的两阶段知识共享策略,为推动产业技术创新联盟知识共享的高效率均衡提供了理论参考。     

On the generic inefficiency of differentiable market games

It is shown that a differentiable market game remains generically inefficient when its strategic outcome function is perturbed smoothly. The proof is based on Thom's transversality theorem and removes any restriction regarding the dimension of the strategy spaces. A converse result is that almost all efficient market games that are competitive are characterized by Bertrand-like non-differentiabilities. Finally a synthesis between the Cournot-and-Bertrand-type approaches to Walrasian equilibrium, as recently developed in the literature, is suggested.     

On the welfare effects of allowing unlimited renegotiation in agency relationships

We study renegotiation in an agency setting where the number of offers and accept/reject decisions parties can make is potentially unlimited. Thus any contract, either on or off the equilibrium path, may be subject to possible renegotiation. We first show that the principal will not be able to gain complete access to the agent’s private information with unlimited renegotiation, unlike when the potential number of renegotiations is finite. Rather the agent either employ a randomized reporting strategy or do not to report at all. We then identify conditions under which expected allocations are most efficient with the contract that induces no agent communication. More significantly, by doing so we also identify conditions under which the parties are made strictly worse off by committing to end renegotiation after a fixed number of rounds. We thank workshop participants at University of California, Irvine, University of Chicago, Duke University, Hong Kong University of Science and Technology, University of Houston, London School of Economics, University of Minnesota, Ohio State University, the Carnegie Mellon Accounting Research Conference, the editor, and an anonymous referee for their helpful comments and suggestions.     

The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.     

Properties and applications of dual reduction

The dual reduction process, introduced by Myerson, allows a finite game to be reduced to a smaller-dimensional game such that any correlated equilibrium of the reduced game is an equilibrium of the original game. We study the properties and applications of this process. It is shown that generic two-player normal form games have a unique full dual reduction (a known refinement of dual reduction) and all strategies that have probability zero in all correlated equilibria are eliminated in all full dual reductions. Among other applications, we give a linear programming proof of the fact that a unique correlated equilibrium is a Nash equilibrium, and improve on a result due to Nau, Gomez-Canovas and Hansen on the geometry of Nash equilibria and correlated equilibria.     

On the Evolution of Pareto‐Optimal Behavior in Repeated Coordination Problems

I characterize the asymptotic behavior of a society facing a repeated‐common‐interest game. In this society, new individuals enter to replace their “parents” at random times. Each entrant has possibly different beliefs about others' behavior than his or her predecessor. A self‐confirming equilibrium (SCE) belief process describes an evolution of beliefs in this society consistent with a self‐confirming equilibrium of the repeated game. The main result shows that for any common‐interest game, the Pareto‐dominant equilibrium is a globally absorbing state of the behavioral dynamics when the SCE beliefs of new entrants satisfy certain independence and full‐support properties. This result does not involve either of the usual assumptions of myopia or large inertia common in evolutionary models, nor is this result possible if only Nash rather than self‐confirming equilibria are considered.