Table of Contents

When and How the Punishment Must Fit the Crime

George J. Mailath, University of Pennsylvania - Department of Economics
Volker Nocke, University of Mannheim - Department of Economics
Lucy White, Harvard Business School - Finance Unit, Centre for Economic Policy Research (CEPR)

Dynamic Moral Hazard Without Commitment

Johannes Horner, Yale University - Cowles Foundation
Larry Samuelson, Yale University - Department of Economics

Bankruptcy Problems: On Rights Arbitration and Game Theory

Louis de Mesnard, IAE Dijon and CREGO (EA 7317), University of Burgundy

Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Heterogeneity

Mario Samano, HEC Montreal
Marc Santugini, HEC Montreal, Institute of Applied Economics, Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi (CIRPÉE)

The Buyer's Role in Improving Supply Chain Energy Efficiency

Jason Quang Nguyen, University of Minnesota - Twin Cities - Carlson School of Management
Karen Lisa Donohue, University of Minnesota - Twin Cities - Carlson School of Management
Mili Mehrotra, University of Minnesota - Twin Cities - Carlson School of Management


GAME THEORY & BARGAINING THEORY eJOURNAL

"When and How the Punishment Must Fit the Crime" Free Download
PIER Working Paper No. 15-008

GEORGE J. MAILATH, University of Pennsylvania - Department of Economics
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VOLKER NOCKE, University of Mannheim - Department of Economics
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LUCY WHITE, Harvard Business School - Finance Unit, Centre for Economic Policy Research (CEPR)
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In repeated normal-form (simultaneous-move) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. By means of examples, we identify two types of settings in which a subgame-perfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation.

"Dynamic Moral Hazard Without Commitment" Free Download
Cowles Foundation Discussion Paper No. 1989

JOHANNES HORNER, Yale University - Cowles Foundation
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LARRY SAMUELSON, Yale University - Department of Economics
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We study a discrete-time model of repeated moral hazard without commitment. In every period, a principal finances a project, choosing the scale of the project and a contingent payment plan for an agent, who has the opportunity to appropriate the returns of a successful project unbeknownst the principal. The absence of commitment is reflected both in the solution concept (perfect Bayesian equilibrium) and in the ability of the principal to freely revise the project's scale from one period to the next. We show that removing commitment from the equilibrium concept is relatively innocuous -- if the players are sufficiently patient, there are equilibria with payoffs low enough to effectively endow the players with the requisite commitment, within the confines of perfect Bayesian equilibrium. In contrast, the frictionless choice of scale has a significant effect on the project's dynamics. Starting from the principal's favorite equilibrium, the optimal contract eventually converges to the repetition of the stage-game Nash equilibrium, operating the project at maximum scale and compensating the agent (only) via immediate payments.

"Bankruptcy Problems: On Rights Arbitration and Game Theory" Free Download

LOUIS DE MESNARD, IAE Dijon and CREGO (EA 7317), University of Burgundy
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We examine ibn Ezra's procedure (Rabinovitch 1973; O'Neill 1982) historically used by him to solve the the Rights Arbitration problem in the general framework of the bankruptcy problems. When the greatest claim is larger than or equal to the estate, the procedure is a maximal game (Aumann 2010). However, when the greatest claim is smaller than the estate, the axioms of efficiency (the whole estate is distributed) and satiation a difficult to reach simultaneously. We discuss both axioms to show that their importance and necessity is radically different. From then, for the part of the estate not covered by the greatest claim, we examine four possible types of procedures: Minimal Overlap Rule, Alcalde et al.'s (2005) iterative generalization, dictator game, and unanimity game. They pose many problems mainly because: (i) only the greatest claimant remains in the game; (ii) playing two different subgames is unrealistic; (iii) some claimants may receive more than they claim, which violates the satiation axiom; (iv) in the Minimal Overlap Rule players play simultaneously a unanimity game and a dictator game; (v) Alcalde et al.'s generalization is is efficient but converges very slowly. This is why we propose an original and different rule, the Series of Nested Unanimity Games (SNUG). We show that it is guarantees efficiency and satiation of all claimants and by respect to the other rules, SNUG is attractively homogenous --- only unanimity games are played ---.

"Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Heterogeneity" Free Download
CIRPEE Working Paper 15-03

MARIO SAMANO, HEC Montreal
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MARC SANTUGINI, HEC Montreal, Institute of Applied Economics, Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi (CIRPÉE)
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We study the long-run market configurations in a quality-ladder dynamic model. Specifically, we assume that the return to investment in quality differs across the firms. That is, for a given level of investment, one firm has a higher probability to raise the quality of the good it produces. We show that the model can generate five different types of long-run market configurations (market collapse, market collapse or monopoly, monopoly, duopoly and monopoly, and duopoly). A high degree of heterogeneity in the return to investment can mitigate the effect of highly reversible investments on the probability of market collapse, giving rise to non-negligible probabilities of observing a duopoly or even dominance of the firm with the lowest return to investment.

"The Buyer's Role in Improving Supply Chain Energy Efficiency" Free Download

JASON QUANG NGUYEN, University of Minnesota - Twin Cities - Carlson School of Management
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KAREN LISA DONOHUE, University of Minnesota - Twin Cities - Carlson School of Management
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MILI MEHROTRA, University of Minnesota - Twin Cities - Carlson School of Management
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This paper analyzes the Energy Efficiency (EE) investment decisions of a capital-constrained manufacturer that services a large industrial buyer. Through a series of game theoretic models, we provide insight into the supplier’s optimal investment decisions and how they are impacted by the buyer’s knowledge of the supplier’s EE opportunities, as well as characteristics of the energy market. We ?nd that buyer knowledge can either help or hinder the supplier’s EE investment level, depending on the cost of the buyer’s alternative supply source and the supplier’s exposure to bankruptcy risk. Utilizing data from Industrial Assessment Centers and the Department of Energy, we run a series of numerical experiments to further isolate the energy market conditions where buyer knowledge is most beneficial and to quantify these associated benefits. Our ?ndings provide insights for policy makers interested in increasing EE investment and reducing the energy efficiency gap that plagues many supply chains.

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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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