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on Game Theory |
| By: | Beatrice Acciaio; Julio Backhoff-Veraguas; Junchao Jia |
| Abstract: | We consider a large population dynamic game in discrete time. The peculiarity of the game is that players are characterized by time-evolving types, and so reasonably their actions should not anticipate the future values of their types. When interactions between players are of mean-field kind, we relate Nash equilibria for such games to an asymptotic notion of dynamic Cournot-Nash equilibria. Inspired by the works of Blanchet and Carlier for the static situation, we interpret dynamic Cournot-Nash equilibria in the light of causal optimal transport theory. Further specializing to games of potential type, we establish existence, uniqueness and characterization of equilibria. Moreover we develop, for the first time, a numerical scheme for causal optimal transport, which is then leveraged in order to compute dynamic Cournot-Nash equilibria. This is illustrated in a detailed case study of a congestion game. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.08786&r=all |
| By: | Helene Mass |
| Abstract: | I investigate the decision problem of a player in a game of incomplete information who faces uncertainty about the other players’ strategies. I propose a new decision criterion — the rational maximin criterion — which works in two steps. First, I assume common knowledge of rationality and eliminate all strategies which are not rationalizable. Second, I apply the maximin criterion. Using this decision criterion, one can derive predictions about outcomes and recommendations for players facing strategic uncertainty. I analyze applications to first-price auctions, contests, and bilateral trade. |
| Keywords: | Incomplete Information, Informational Robustness, Rationalizability |
| JEL: | D81 D82 D83 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_157&r=all |
| By: | Constantinos Daskalakis; Maxwell Fishelson; Brendan Lucier; Vasilis Syrgkanis; Santhoshini Velusamy |
| Abstract: | We identify the first static credible mechanism for multi-item additive auctions that achieves a constant factor of the optimal revenue. This is one instance of a more general framework for designing two-part tariff auctions, adapting the duality framework of Cai et al [CDW16]. Given a (not necessarily incentive compatible) auction format $A$ satisfying certain technical conditions, our framework augments the auction with a personalized entry fee for each bidder, which must be paid before the auction can be accessed. These entry fees depend only on the prior distribution of bidder types, and in particular are independent of realized bids. Our framework can be used with many common auction formats, such as simultaneous first-price, simultaneous second-price, and simultaneous all-pay auctions. If all-pay auctions are used, we prove that the resulting mechanism is credible in the sense that the auctioneer cannot benefit by deviating from the stated mechanism after observing agent bids. If second-price auctions are used, we obtain a truthful $O(1)$-approximate mechanism with fixed entry fees that are amenable to tuning via online learning techniques. Our results for first price and all-pay are the first revenue guarantees of non-truthful mechanisms in multi-dimensional environments; an open question in the literature [RST17]. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.06702&r=all |
| By: | Akshay Krishnamurthy; Thodoris Lykouris; Chara Podimata |
| Abstract: | Standard game-theoretic formulations for settings like contextual pricing and security games assume that agents act in accordance with a specific behavioral model. In practice however, some agents may not prescribe to the dominant behavioral model or may act in ways that are arbitrarily inconsistent. Existing algorithms heavily depend on the model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrarily irrational agents. \emph{How do we design learning algorithms that are robust to the presence of arbitrarily irrational agents?} We address this question for a number of canonical game-theoretic applications by designing a robust algorithm for the fundamental problem of multidimensional binary search. The performance of our algorithm degrades gracefully with the number of corrupted rounds, which correspond to irrational agents and need not be known in advance. As binary search is the key primitive in algorithms for contextual pricing, Stackelberg Security Games, and other game-theoretic applications, we immediately obtain robust algorithms for these settings. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis, and may be of independent algorithmic interest. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.11650&r=all |
| By: | Zuzana Brokesova (University of Economics in Bratislava); Cary Deck (University of Alabama; Economic Science Institute, Chapman University); Jana Peliova (University of Economics in Bratislava) |
| Abstract: | The newsvendor problem is a workhorse model in operation management research. We introduce a related game that operates in the price dimension rather than the inventory dimension: the price gouging game. Using controlled laboratory experiments, we compare news vending and price gouging behavior. We replicate the standard pull-to-center effect for news vending and find that the equivalent pattern occurs with price gouging. Further, we find that the pull-to-center is asymmetric both for newsvendors and price gougers. More broadly, the experimental results reveal that choices are similar across the theoretically isomorphic games, suggesting that observed behavior in newsvendor experiments is representative of a broader class of games and not driven by the operations context that is often used in newsvendor experiments. Finally, we do not find evidence that behavior in these games is systemically affected by sex, risk attitude, or cognitive reflection. |
| Keywords: | Behavioral Operations; Price Gouging; Newsvendor Game; Inventory; Pull-to-Center Effect |
| JEL: | C9 D2 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-09&r=all |
| By: | Sylvain Béal (CRESE, Université de Franche-comté); Sylvain Ferrières (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne) |
| Abstract: | We study cooperative games with a priority structure modeled by a poset on the agent set. We introduce the Priority value, which splits the Harsanyi dividend of each coalition among the set of its priority agents, i.e. the members of the coalition over which no other coalition member has priority. This allocation shares many desirable properties with the classical Shapley value: it is efficient, additive and satisfies the null agent axiom, which assigns a null payoff to any agent with null contributions to coalitions. We provide two axiomatic characterizations of the Priority value which invoke both classical axioms and new axioms describing various effects that the priority structure can impose on the payoff allocation. Applications to queueing and bankruptcy problems are discussed. |
| Keywords: | Priority structure, Shapley value, Priority value, necessary agent, Harsanyi solution, queueing problems, bankruptcy problems. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2020-02&r=all |
| By: | Masaaki Fujii (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo) |
| Abstract: | In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents 1 ≤ i ≤ N are interacting through the market price. Adopting a mean fild game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf473&r=all |
| By: | Serhat Dogan; Emin Karagözoðlu; Kerim Keskin; Cagri Saglam; Emin Karagözoglu |
| Abstract: | We study bribing in a sequential team contest with multiple pairwise battles. We allow for asymmetries in winning prizes and marginal costs of effort; and we characterize the conditions under which (i) a player in a team is offered a bribe by the owner of the other team and (ii) she accepts the bribe. We show that these conditions depend on the ratios of players’ winning prizes and marginal costs of effort: the team owner chooses to bribe the player with the most favorable winning prize to marginal cost of effort ratio, and offer a bribe that leaves her indifferent between accepting (and exerting zero effort) and not accepting (and exerting her optimal effort). In some cases, the competition between players and the negative consequences of one player receiving a bribe on the team performance can drag down equilibrium bribe to zero. We also study the impact of changes in winning prizes and marginal costs of effort on equilibrium bribing behavior. |
| Keywords: | bribing, contest games, pairwise battles, team contests |
| JEL: | C72 D73 D74 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8096&r=all |
| By: | Oliver Bos; Martin Pollrich |
| Abstract: | We study optimal auctions in a symmetric private values setting, where bidders’ care about winning the object and a receiver’s inference about their type. We reestablish revenue equivalence when bidders’ signaling concerns are linear, and the auction makes participation observable via an entry fee. With convex signaling concerns, optimal auctions are fully transparent: every standard auction, which reveals all bids yields maximal revenue. With concave signaling concerns there is no general revenue ranking. We highlight a trade-off between maximizing revenue derived from signaling, and extracting information from bidders. Our methodology combines tools from mechanism design with tools from Bayesian persuasion. |
| Keywords: | optimal auctions, revenue equivalence, Bayesian persuasion, information design |
| JEL: | D44 D82 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_158&r=all |
| By: | Timothy N. Cason; Robertas Zubrickas |
| JEL: | C72 C92 H41 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1319&r=all |
| By: | Tobias Salz; Emanuel Vespa |
| Abstract: | We evaluate dynamic oligopoly estimators with laboratory data. Using a stylized en-try/exit game, we estimate structural parameters under the assumption that the data are generated by a Markov-perfect equilibrium (MPE) and use the estimates to predict counterfactual behavior. The concern is that if the Markov assumption was violated one would mispredict counterfactual outcomes. The experimental method allows us to compare predicted behavior for counterfactuals to true counterfactuals implemented as treatments. Our main finding is that counterfactual prediction errors due to collusion are in most cases only modest in size. |
| JEL: | L10 L13 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26765&r=all |
| By: | Bhan, Aditya; Kabiraj, Tarun |
| Abstract: | The paper shows that in the absence of external sponsorship, strategic cooperation between two outfits has no impact on terror activity, if neither outfit is resource-constrained a priori. If only one outfit is resource-constrained a priori, inter-group cooperation increases terror activity if and only if there is sufficient resource-asymmetry between the outfits. Further, if both outfits are resource-constrained a priori, then cooperation may increase or decrease terror activity, depending on parametric asymmetries. Finally, it is demonstrated that while cooperation can neutralize the impact of strategic external sponsorship on terror activity and thereby remove the incentive for its provision, there is always some external sponsorship mechanism which can be utilized to enhance terror activity. |
| Keywords: | Terror outfit; Terror attacks; Non-cooperative competition; Outfit cooperation; Sponsorship fund; Counter terrorism |
| JEL: | C71 C72 D74 H79 |
| Date: | 2020–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98484&r=all |
| By: | Benjamin Golub |
| Abstract: | This note presents a simple overlapping-generations (OLG) model of the transmission of a trait, such as a culture. Initially, some fraction of agents carry the trait. In each time period, young agents are ``born'' and are influenced by some older agents. Agents adopt the trait only if at least a certain number of their influencers have the trait. This influence may occur due to rational choice (e.g., because the young agents are playing a coordination game with old agents who are already committed to a strategy), or for some other reason. Our interest is in how the process of social influence unfolds over time, and whether a trait will persist or die out. We characterize the dynamics of the fraction of active agents and relate the analysis to classic results on branching processes and random graphs. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.03569&r=all |