Games with capacity manipulation: incentives and Nash equilibria

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced.

[1]  Marilda Sotomayor,et al.  The stability of the equilibrium outcomes in the admission games induced by stable matching rules , 2008, Int. J. Game Theory.

[2]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[3]  Antonio Romero-Medina,et al.  Non-Revelation Mechanisms in Many-to-One Markets , 2013, Games Econ. Behav..

[4]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[5]  David A. Freedman,et al.  Machiavelli and the Gale-Shapley Algorithm , 1981 .

[6]  Tayfun Sönmez,et al.  Manipulation via Capacities in Two-Sided Matching Markets , 1997 .

[7]  Antonio Romero-Medina,et al.  Simple Mechanisms to Implement the Core of College Admissions Problems , 2000, Games Econ. Behav..

[8]  David Gale,et al.  Ms. Machiavelli and the Stable Matching Problem , 1985 .

[9]  Onur Kesten.  On two kinds of manipulation for school choice problems , 2012 .

[10]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[11]  Tayfun Sönmez,et al.  Comparing Mechanisms by their Vulernability to Manipulation , 2008 .

[12]  H. Ergin.  Efficient Resource Allocation on the Basis of Priorities , 2002 .

[13]  Andrew Postlewaite,et al.  Feasible Nash Implementation of Social Choice Rules When the Designer Does not Know Endowments or Production Sets , 1995 .

[14]  Ismail Saglam,et al.  Games of capacity allocation in many-to-one matching with an aftermarket , 2009, Soc. Choice Welf..

[15]  Marilda Sotomayor,et al.  Reaching the core of the marriage market through a non-revelation matching mechanism , 2003, Int. J. Game Theory.

[16]  M. Utku Ünver,et al.  Games of Capacity Manipulation in Hospital-intern Markets , 2006, Soc. Choice Welf..

[17]  José R. Correa,et al.  Decision , Risk and Operations Working Papers Series The cost of moral hazard and limited liability in the principal-agent problem , 2010 .

[18]  Parag A. Pathak,et al.  The New York City High School Match , 2005 .

[19]  Nicolas Figueroa,et al.  Loyalty Inducing Programs and Competition with Homogeneous Goods , 2008 .

[20]  Tayfun Sönmez.  Games of Manipulation in Marriage Problems , 1997 .

[21]  Kojima Fuhito,et al.  When Can Manipulations be Avoided in Two-Sided Matching Markets? -- Maximal Domain Results , 2007 .

[22]  Tayfun Sönmez,et al.  Implementation of college admission rules , 1997 .

[23]  Antonio Romero-Medina,et al.  Acyclicity and Singleton Cores in Matching Markets , 2012 .

[24]  A. Roth.  The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics , 2002 .

[25]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .

[26]  David Gale,et al.  Some remarks on the stable matching problem , 1985, Discret. Appl. Math..

[27]  Lars Ehlers,et al.  Manipulation via capacities revisited , 2010, Games Econ. Behav..