Table of Contents

Long-Term Relationships: Static Gains and Dynamic Inefficiencies

David Hemous, INSEAD
Morten Olsen, University of Navarra, IESE Business School

Lottery Allocations and Games for Public Rental Apartments

Zhan Wang, Sichuan University - School of Economics
Jinpeng Ma, Rutgers University-Camden
Hongwei Zhang, Sichuan University - School of Economics

Game Theoretic Models for Energy Production

Michael Ludkovski, University of California, Santa Barbara
Ronnie Sircar, Princeton University - Department of Operations Research and Financial Engineering

Bilateral Trade with Loss-Averse Agents

Jean-Michel Benkert, University of Zurich - Department of Economics

The Efficiency of Bargaining with Many Items

Matthew O. Jackson, Stanford University - Department of Economics, Santa Fe Institute, Canadian Institute for Advanced Research (CIFAR)
Hugo Sonnenschein, Stanford University - Department of Economics
Yiqing Xing, Stanford University, Department of Economics

Group Size Can Have Positive, Negative, or Even Curvilinear Effect on Cooperation Depending on How the Benefit for Full Cooperation Varies as a Function of the Group Size

Valerio Capraro, Center for Mathematics and Computer Science
Helene Barcelo, Mathemathical Sciences Research Institute (MSRI)


GAME THEORY & BARGAINING THEORY eJOURNAL

"Long-Term Relationships: Static Gains and Dynamic Inefficiencies" Fee Download
CEPR Discussion Paper No. DP10490

DAVID HEMOUS, INSEAD
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MORTEN OLSEN, University of Navarra, IESE Business School
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Do contractual frictions matter when firms are engaged in repeated interactions? This paper argues that long-term relationships, which allow firms to (partly) overcome the static costs associated with low contractibility, will under certain circumstances create dynamic inefficiencies. We consider the repeated interaction between final good producers and intermediate input suppliers, where the provision of the intermediate input is noncontractible. A producer/supplier pair can be a good match or a bad match, with bad matches featuring lower productivity. This allows us to build a cooperative equilibrium where producers can switch suppliers and start cooperation immediately with new suppliers. Every period, one supplier has the opportunity to innovate, and in the baseline model, innovations are imitated after one period. We show that (i) innovations need to be larger to break up existing relationships in the cooperative equilibrium than in either a set-up where the input is contractible or when we preclude cooperation in long-term relationships, (ii) the rate of innovation in the cooperative equilibrium is lower than in the contractible case, and may even be lower than in the non-cooperative equilibrium and (iii) cooperation may reduce welfare. Next, we assume that the frontier technology diffuses slowly to suppliers (instead of after one period). In that case, for sufficiently slow diffusion, the innovation rate in the cooperative equilibrium may be higher than even in the contractible case. Finally, we show that cooperation may also increase relationship specific innovations.

"Lottery Allocations and Games for Public Rental Apartments" Free Download

ZHAN WANG, Sichuan University - School of Economics
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JINPENG MA, Rutgers University-Camden
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HONGWEI ZHANG, Sichuan University - School of Economics
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A lottery is often used to allocate public rental apartments in practice. The existing random assignments in the literature do not apply to public rental apartments because practical constraints are more restrictive. We provide a lottery-TTC algorithm to find a lottery allocation that has two desired properties of individual stability (IS) and coalitional stability (CS). The new IS notion is proposed to resolve the nonexistence of an envy-free allocation. Further more, we provide a lottery game and show that any IS allocation induces a Nash equilibrium in pure strategies, and vice versa. We also investigate a restrictive domain where a strict envy-free (SEF) allocation does exist. In that domain, we show that the SEF allocation is the unique IS and CS allocation and induces a random assignment that is Pareto optimal and equal to the pseudo market random assignment found by Hylland and Zeckhauser (1979). Our lottery-TTC algorithm provides a simple method to implement the pseudo market competitive mechanism in Hylland and Zeckhauser (1979) in Nash equilibrium in pure strategies on the restrictive domain.

"Game Theoretic Models for Energy Production" Free Download

MICHAEL LUDKOVSKI, University of California, Santa Barbara
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RONNIE SIRCAR, Princeton University - Department of Operations Research and Financial Engineering
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We give a selective survey of oligopoly models for energy production which capture to varying degrees issues such as exhaustibility of fossil fuels, development of renewable sources, exploration and new technologies, and changing costs of production. Our main focus is on dynamic Cournot competition with exhaustible resources. We trace the resulting theory of competitive equilibria and discuss some of the major emerging strands, including competition between renewable and exhaustible producers, endogenous market phase transitions, stochastic differential games with controlled jumps, and mean field games.

"Bilateral Trade with Loss-Averse Agents" Free Download
University of Zurich, Department of Economics, Working Paper No. 188

JEAN-MICHEL BENKERT, University of Zurich - Department of Economics
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We study the bilateral trade problem put forward by Myerson and Satterthwaite (1983) under the assumption that agents are loss-averse. We use the model developed by Kőszegi and Rabin (2006, 2007) to find optimal mechanisms for the minimal subsidy, revenue maximization and welfare maximization problem. In both, welfare and revenue maximizing mechanisms, the designer induces less trade in the presence of loss-aversion. Intuitively, the designer is providing the agents with partial insurance. Moreover, the designer optimally provides the agents with full insurance in the money dimension, i.e. she offers deterministic transfers. Another implication of loss-aversion is that it increases the severity of the impossibility problem, that is, the minimal subsidy needed to induce materially efficient trade is higher. All results display robustness to the exact specification of the reference point. We also provide some general mechanism design results.

"The Efficiency of Bargaining with Many Items" Free Download

MATTHEW O. JACKSON, Stanford University - Department of Economics, Santa Fe Institute, Canadian Institute for Advanced Research (CIFAR)
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HUGO SONNENSCHEIN, Stanford University - Department of Economics
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YIQING XING, Stanford University, Department of Economics
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For an important class of alternating-offer bargaining problems with significant two-sided asymmetric information, we demonstrate that all sequential equilibria are efficient or approximately efficient. We focus on the case in which the bargaining problem contains many aspects, the value of each of which is private information, but which aggregate to an overall surplus from trade that is approximately known. The results may help explain why so many situations with significant asymmetric information exhibit little departure from first best efficiency (e.g., time lost to labor negotiations is negligible world-wide).

"Group Size Can Have Positive, Negative, or Even Curvilinear Effect on Cooperation Depending on How the Benefit for Full Cooperation Varies as a Function of the Group Size" Free Download

VALERIO CAPRARO, Center for Mathematics and Computer Science
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HELENE BARCELO, Mathemathical Sciences Research Institute (MSRI)
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In a world in which many pressing global issues require large scale cooperation, understanding the group size effect on cooperative behavior is a topic of central importance. Yet, the nature of this effect remains largely unknown, with lab experiments insisting that it is either positive or negative or null, and field experiments suggesting that it is instead curvilinear. Here we shed light on this apparent contradiction by showing that one can recreate all these effects in the lab by varying a single parameter. Specifically, if the benefit for full cooperation remains constant as a function of the group size, then larger groups are less cooperative; if it increases linearly with the size of the group, then larger groups are more cooperative; however, in the more realistic scenario in which the natural output limits of the public good imply that the benefit of cooperation increases fast for early contributions and then decelerates, one may get a curvilinear effect according to which intermediate-size groups cooperate more than smaller groups and more than larger groups. Our findings help fill the gap between lab experiments and field experiments and suggest concrete ways to promote large scale cooperation among people.

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About this eJournal

This eJournal distributes working and accepted paper abstracts of empirical and theoretical papers on game theory, defined as the study of the strategic interaction among rational agents in competitive and cooperative environments, and bargaining theory, defined as a situation in which two or more players have a common interest to co-operate, but have conflicting interests over exactly how to co-operate. The topics in this eJournal include all of the subjects in Section C7 of the JEL classification system.

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