Walrasian equilibrium: An alternate proof of existence and lattice structure
Komal Malik
We consider a model of two-sided matching market where buyers and sellers trade indivisible goods with the feature that each buyer has unit demand and seller has unit supply. The result of the existence of Walrasian equilibrium and lattice structure of equilibrium price vectors is known. We provide an alternate proof for existence and lattice structure using Tarksi's fixed point theorem.
Börgers's Open Question Resolved
Siyang Xiong
Focusing on stochastic finite-action mechanisms, we study implementation in undominated strategies and iteratively undominated strategies. We establish both possibility and impossibility results that resolve the open question in Börgers (1995). Contrary to the conventional understanding that positive results on Nash implementation need separability, quasilinearity, or infinite action sets, we provide -- to our knowledge -- the first positive result beyond those demanding assumptions.
Justified Fairness in House Allocation Problems: two Characterizations of Strategy-proof Mechanisms
Di Feng, Jacob Coreno
We consider the house allocation problems with strict preferences, where monetary transfers are not allowed. We propose two properties in the spirit of justified fairness. Interestingly, together with other well-studied properties (strategy-proofness and non-bossiness), our two new properties identify serial dictatorships and sequential dictatorships, respectively.
Expert Classification Aggregation
Federico Fioravanti
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories by aggregating the individual classifications, and no category can be left empty. An aggregator satisfies \emph{Expertise} if individuals are decisive either over the classification of a given object, or the classification into a given category. We show that requiring an aggregator to satisfy \emph{Expertise} (or variants of it) and be either unanimous or independent leads to numerous impossibility results.
Comment on Matsushima, Miyazaki, and Yagi (2010) "Role of Linking Mechanisms in Multitask Agency with Hidden Information"
Ian Ball, Deniz Kattwinkel
We correct a gap in the proof of Theorem 2 in Matsushima et al. (2010).
Repeated Bidding with Dynamic Value
Benjamin Heymann, Alexandre Gilotte, Rémi Chan-Renous
We consider a repeated auction where the buyer's utility for an item depends on the time that elapsed since his last purchase. We present an algorithm to build the optimal bidding policy, and then, because optimal might be impractical, we discuss the cost for the buyer of limiting himself to shading policies.
Pulse in collapse: a game dynamics experiment
Wang Yijia, Wang Zhijian
The collapse process is a constitutional sub-process in the full finding Nash equilibrium process. We conducted laboratory game experiments with human subjects to study this process. We observed significant pulse signals in the collapse process. The observations from the data support the completeness and the consistency of the game dynamics paradigm.
Bauer's Maximum Principle for Quasiconvex Functions
Ian Ball
This note shows that in Bauer's maximum principle, the assumed convexity of the objective function can be relaxed to quasiconvexity.
Strategies in deterministic totally-ordered-time games
Tomohiko Kawamori
We consider deterministic totally-ordered-time games. We present three axioms for strategies. We show that for any tuple of strategies that satisfy the axioms, there exists a unique complete history that is consistent with the strategy tuple.
Rationalizable Implementation of Social Choice Functions: Complete Characterization
Siyang Xiong
We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented.
Posterior Probabilities: Dominance and Optimism
Sergiu Hart, Yosef Rinott
The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.
Sequential Cursed Equilibrium
Shani Cohen, Shengwu Li
We propose an extensive-form solution concept, with players that neglect information from hypothetical events, but make inferences from observed events. Our concept modifies cursed equilibrium (Eyster and Rabin, 2005), and allows that players can be 'cursed about' endogenous information.
The Existence of Equilibrium Flows
Alfred Galichon, Larry Samuelson, Lucas Vernet
Galichon, Samuelson and Vernet (2022) introduced a class of problems, equilibrium flow problems, that nests several classical economic models such as bipartite matching models, minimum-cost flow problems and hedonic pricing models. We establish conditions for the existence of equilibrium prices in the equilibrium flow problem, in the process generalizing Hall's theorem.
Ex-post implementation with interdependent values
Saurav Goyal, Aroon Narayanan
We characterize ex-post implementable allocation rules for single object auctions under quasi-linear preferences with convex interdependent value functions. We show that requiring ex-post implementability is equivalent to requiring that the allocation rule must satisfy a condition that we call eventual monotonicity (EM), which is a weakening of monotonicity, a familiar condition used to characterize dominant strategy implementation.
Stable matching: an integer programming approach
Chao Huang
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete matching market when firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.
A closed-form solution to the risk-taking motivation of subordinated debtholders
Yuval Heller, SharonPeleg-Lazar, Alon Raviv
Black and Cox (1976) claim that the value of junior debt is increasing in asset risk when the firm's value is low. We show, using closed-form solution, that the junior debt's value is hump-shaped. This has interesting implications for the market-discipline role of banks' junior debt.
The converse envelope theorem
Ludvig Sinander
I prove an envelope theorem with a converse: the envelope formula is equivalent to a first-order condition. Like Milgrom and Segal's (2002) envelope theorem, my result requires no structure on the choice set. I use the converse envelope theorem to extend to general outcomes and preferences the canonical result in mechanism design that any increasing allocation is implementable, and apply this to selling information.
Bayesian Elicitation
Mark Whitmeyer
We study how a decision-maker can acquire more information from an agent by reducing her own ability to observe what the agent transmits. In a large class of binary-action games, opacity design is just as good as full commitment to actions and also guarantees that ex ante information acquisition always benefits the receiver, even though without opacity design this learning might actually lower the receiver's expected payoff.
Coalitions in Repeated Games
S. Nageeb Ali, Ce Liu
This paper proposes a framework and solution concept for repeated coalitional behavior. We model history-dependent schemes that deter coalitions from blocking using continuation promises and punishments. We evaluate the effectiveness of these schemes across a range of settings, and apply our results to repeated matching and negotiations.
The Losses from Integration in Matching Markets can be Large
Josué Ortega
Although the integration of two-sided matching markets using stable mechanisms generates expected gains from integration, I show that there are worst-case scenarios in which these are negative. The losses from integration can be large enough that the average rank of an agent's spouse decreases by 37.5% of the length of their preference list in any stable matching mechanism.