Table of Contents

The Paradox of Grading Systems

Steven J. Brams, New York University (NYU) - Wilf Family Department of Politics
Richard Potthoff, Duke University - Department of Political Science

Alliance Formation in Contests with Incomplete Information

Lars Peter Metzger, Independent

The Logic of Normal-Form Games

Gabriel Frahm, Helmut Schmidt University

Communication and Coordination in a Two-Stage Game

Tjasa Bjedov, University of Fribourg
Thierry Madiès, University of Fribourg (Switzerland) - Faculty of Economics and Social Science
Marie Claire Villeval, National Center for Scientific Research (CNRS) - Institute of Economic Theory and Analysis (GATE), Institute for the Study of Labor (IZA)

Unintended Consequences of Promotions: Should Managers Worry About Consumer Stockpiling?

Manish Gangwar, Indian School of Business (ISB), Hyderabad
Nanda S. Kumar, University of Texas at Dallas - Department of Marketing
Ram C. Rao, The University of Texas at Dallas, Naveen Jindal School of Management

Coalitional Approaches to Collusive Agreements in Oligopoly Games

Sergio Currarini, University of Leicester - Department of Economics, Ca Foscari University of Venice - Department of Economics
Marco A. Marini, Sapienza Università di Roma , CREI, University Rome III


GAME THEORY & BARGAINING THEORY eJOURNAL

"The Paradox of Grading Systems" Free Download

STEVEN J. BRAMS, New York University (NYU) - Wilf Family Department of Politics
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RICHARD POTTHOFF, Duke University - Department of Political Science
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We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, such as approval voting, in which voters can give two grades — approve (1) or not approve (0) — to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.

"Alliance Formation in Contests with Incomplete Information" Free Download
Ruhr Economic Paper No. 544

LARS PETER METZGER, Independent
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This paper studies a contest in which players with unobservable types may form an alliance in a pre-stage of the game to join their forces and compete for a prize. We characterize the pure strategy equilibria of this game of incomplete information. We show that if the formation of an alliance is voluntary, players do not reveal private information in the process of alliance formation in any equilibrium. In this case there exists a pooling equilibrium without alliances with a unique effort choice in the contest and there exist equilibria in which all types prefer to form an alliance. If the formation of an alliance can be enforced by one player with positive probability there exists an equilibrium in which only the low types prefer to form an alliance.

"The Logic of Normal-Form Games" Free Download

GABRIEL FRAHM, Helmut Schmidt University
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The Nash equilibrium leads to solutions that are logically inconsistent under the typical common-knowledge assumption of noncooperative game theory. A new concept of strategic equilibrium is introduced and it is shown that every normal-form game either has a unique equilibrium or the equilibrium is nonexistent. The main result states that the solution of every nondegenerate normal-form game corresponds to the unique equilibrium, provided the common-knowledge assumption is satisfied. This solves the multiple-solution problem, which is a deep and longstanding problem of noncooperative game theory. The probabilistic framework used in this work is quite general and able to explain different forms of strategic interaction that frequently occur in real-life situations. Further, the conditions under which the Nash equilibrium can serve as an instrument for localizing the set of rational solutions are clarified. It turns out that for this purpose, common knowledge is superfluous.

"Communication and Coordination in a Two-Stage Game" Free Download

TJASA BJEDOV, University of Fribourg
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THIERRY MADIÈS, University of Fribourg (Switzerland) - Faculty of Economics and Social Science
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MARIE CLAIRE VILLEVAL, National Center for Scientific Research (CNRS) - Institute of Economic Theory and Analysis (GATE), Institute for the Study of Labor (IZA)
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We study the impact of communication on behavior in a two-stage coordination game with asymmetric payoffs. We test experimentally whether individuals can avoid a head-to-head confrontation by means of coordinated strategies. In particular we analyze whether and how quickly a conflict-avoidance take-turn strategy can emerge. First, our results show that players learn to solve the conflict by choosing opposite options at both stages of the game. Second, many adopt a take-turn strategy to sustain coordination over time and alleviate the inequality induced by the asymmetry of payoffs. Third, communication increases the likelihood of conflict resolution even when a single pair member has the right to communicate.

"Unintended Consequences of Promotions: Should Managers Worry About Consumer Stockpiling?" Free Download

MANISH GANGWAR, Indian School of Business (ISB), Hyderabad
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NANDA S. KUMAR, University of Texas at Dallas - Department of Marketing
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RAM C. RAO, The University of Texas at Dallas, Naveen Jindal School of Management
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Increase in sales due to promotions could come at the expense of competitors; such sales come from consumers who have relatively weak brand preferences. Increased sales from consumers with strong brand preferences are likely to be at the expense of the promoted brand. In other words, brand loyal consumers can take advantage of promotions to stockpile for future consumption. Thus, loyal consumers who would be otherwise willing to buy at high prices can strategically stockpile at low prices. What is its impact on firms’ profits? How should firms adapt to consumer stockpiling? To answer these questions we model a duopoly competing for loyal and switching consumers.

In contrast to extant finding that stockpiling by switching consumers does not affect firms’ profitability, we find that stockpiling by loyal consumers (empirically who are found more likely to stockpile) indeed reduces firms’ long-run profits. We also find that even when stockpiling may induce higher consumption, it reduces but does not eliminate losses. Furthermore, we establish an upper bound on the loss due to loyal consumers’ stockpiling. Surprisingly, we find that it amounts to a relatively small percentage of profits. We also obtain a novel finding on mixed strategies that firms’ equilibrium pricing distributions can have mass points in the interior of the support. Our results also offer several counter-intuitive insights of relevance to managers.

"Coalitional Approaches to Collusive Agreements in Oligopoly Games" Fee Download
The Manchester School, Vol. 83, Issue 3, pp. 253-287, 2015

SERGIO CURRARINI, University of Leicester - Department of Economics, Ca Foscari University of Venice - Department of Economics
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MARCO A. MARINI, Sapienza Università di Roma , CREI, University Rome III
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In this paper we review a number of coalitional solution concepts for the analysis of cartel and merger stability in oligopoly. We show that, although so far the industrial organization and the cooperative game theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter?connected. We show that different assumptions on the behaviour and on the timing of the coalitions of firms yield very different results on the associations of firms which are stable. We conclude by reviewing some recent extensions of the coalitional analysis to oligopolistic markets with heterogeneous firms and incomplete information.

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