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Game Theory

Paper Session

Friday, Jan. 6, 2023 8:00 AM - 10:00 AM (CST)

Hilton Riverside, Chart C
Hosted By: American Economic Association
  • Chair: Jiabin Wu, University of Oregon

Keep ’Em Coming: Detecting and Nurturing Loyalty

Anna Sanktjohanser
,
Yale University
Johannes Horner
,
Yale University

Abstract

We consider a continuous-time game between a buyer and a seller.
The buyer privately knows how often he needs to trade. When he does,
he can choose to either engage with the seller, who chooses what utility
to supply, or search for an alternative. Because time is informative, the
seller learns and adjusts her behavior over time. Without commitment,
in the Markov perfect equilibrium, the seller starts with a pooling offer,
before experimenting with occasional separating offers. Her payoff is
non-monotone –in fact, quasi-convex– in her belief about the buyer’s
type. With commitment, the seller can take advantage of limited-time
offers to extract all the buyer’s surplus.

Decentralized Matching with Transfers: Experimental and Noncooperative Analyses

Simin He
,
Shanghai University of Finance and Economics
Jiabin Wu
,
University of Oregon
Hanzhe Zhang
,
Michigan State University

Abstract

We experimentally examine the Becker-Shapley-Shubik two-sided matching model. In the experiment,
the aggregate outcomes of matching and surplus are affected by whether the pairwise Nash-Rubinstein
bargaining outcome of equal surplus division is stable and, to a lesser extent, by whether efficient
matching is assortative, while the canonical cooperative theory predicts no effect. In balanced markets,
that is, markets with equal numbers of participants on both sides, individual payoffs in our and
others’ experiments cannot be explained by existing refinements of the core, but are consistent with
the predictions of our noncooperative model. In imbalanced markets, that is, markets with unequal
numbers of participants on the two sides, noncompetitive outcomes, where subjects on the long side
do not fully compete, are not captured by the canonical cooperative model, but are included in the set
of predictions in our noncooperative model.

Quantal Response Equilibrium with Symmetry: Representation and Applications

Evan Friedman
,
University of Essex
Felix Mauersberger
,
University of Bonn

Abstract

We study an axiomatic variant of quantal response equilibrium (QRE) for normal form games that augments the regularity axioms (Goeree et al., 2005) with various forms of “symmetry” across players and actions. The model refines regular QRE, implies bounds on logit QRE, and is tractable in many applications. The main result is a representation theorem that characterizes the model’s set-valued predictions by taking unions and intersections of simple sets. We completely characterize the predictions for (almost) all 2x2 games, a corollary of which is to show, in coordination games, which Nash equilibrium is selected by the principal branch of the logit correspondence. As applications, we consider three classic games: public goods provision with heterogenous costs of participation, jury voting with unanimity, and the infinitely repeated prisoner’s dilemma. For each, we characterize all equilibria within a particular large class. An analysis of existing experimental data shows the potential, and limitations, of the model.

All-in fighting

Marco Serena
,
Max Planck Institute for Tax Law and Public Finance
Stefano Barbieri
,
Tulane University

Abstract

How does reputation building affect the intensity of repeated conflicts? We propose a model where players fight in a sequence of battles and privately know whether they are rational (and choose fighting efforts so as to maximize payoff) or automatons locked into fighting "all-in" in every battle. Rational players may pretend to be automatons and fight all-in in early battles as doing so buys a beneficial "all-in look" that intimidates rivals in future battles. We study such dynamics. In the unique symmetric equilibrium, a rational player has strictly positive payoff only if she monopolizes, among all players, the reputation for fighting all-in. In a period with reputational oligopoly, a war of attrition to become the reputational monopolist may yield overdissipation (expected fighting efforts exceeding the per-period prize). In a period with reputational monopoly, overdissipation never happens and the monopolist mixes between fighting all-in to boost her reputation tomorrow and a continuum of non-all-in fighting efforts to cash in on her reputation today. While a monopoly may last indefinitely, an oligopoly does not. Applications include turf wars, sea piracy, conflicts, and litigation.

Interim Strategy-Proof Mechanisms

Tangren Feng
,
Bocconi University
Qinggong Wu
,
Hong Kong University of Science and Technology

Abstract

We study a new robustness concept in mechanism design with interdependent values: Interim Strategy-Proofness (ISP). It requires that truth-telling is an interim dominant strategy for each agent, i.e., conditional on an agent’s own private information, the truth-telling maximizes her interim expected payoff for all possible strategies the other agents could use. We first show that ISP mechanisms are higher-order belief-free: an agent’s first-order belief is sufficient to determine whether a strategy is interim dominant, whereas higher-order beliefs do not matter. We then provide full characterizations of ISP mechanisms in two classical settings: single unit auctions and binary collective decision-makings.

Jump Bidding as a Signaling Game

Haimeng Zhang
,
Cornell University

Abstract

This paper studies jump bidding in an ascending-bid auction with affiliated values using a multi-round signaling model. Bidders communicate their private information with one another via the sizes of jump bids. These signals are credible since bidders with lower private information incur a higher ex ante cost for choosing a jump bid with any given size. This prevents the bidders with lower private information from mimicking those with higher private information. In equilibrium, the signaling model predicts that the size of a jump bid placed each round is bounded above by a strategy that is equivalent to one in a first-price sealed-bid auction. The expected revenue to the seller is reduced due to bidders’ abilities to send signals through jump bidding. Using data from a spectrum auction held by the Federal Communications Commission in the United States, the mean valuation estimated using the signaling model is higher compared to that of the “open exit” model. This implies that if bidders are indeed using jump bids as signals, ignoring it leads to estimates of the mean values that are biased downwards. This result is consistent with the prediction of the theoretical model that bidders pay lower prices with jump bidding than in an open exit auction. I estimate that if jump bidding was prohibited, the government could have had 8% higher revenues from the auction.
JEL Classifications
  • C7 - Game Theory and Bargaining Theory