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on Game Theory |
| By: | Miryana Grigorova (LPSM, UPCit\'e); Marie-Claire Quenez (LPSM, UPCit\'e); Yuan Peng |
| Abstract: | In this paper, we study a non-zero-sum game with two players, where each of the players plays what we call Bermudan strategies and optimizes a general non-linear assessment functional of the pay-off. By using a recursive construction, we show that the game has a Nash equilibrium point. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.01086&r=gth |
| By: | Axel Anderson (Department of Economics, Georgetown University); Jeremy Rosen (Department of Economics, Georgetown University); John Rust (Department of Economics, Georgetown University); Kin-ping Wong (Digonex) |
| Abstract: | Are the serves of the world’s best tennis pros consistent with the theoretical predictions of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the receiver’s left, right or body) with data from an online database called the Match Charting Project. Using a new methodology, we test and decisively reject a key implication of a mixed strategy Nash equilibrium, namely, that the probability of winning a service game is the same for all serve directions. We also use dynamic programming (DP) to numerically solve for the best-response serve strategies in models of the service game of tennis estimated for individual server-receiver pairs, such as Novak Djokovic serving to Rafael Nadal. We show that for most elite professional servers, the DP serve strategy significantly increases their service game win probability compared to the mixed strategies they actually use, which we estimate using flexible reduced-form logit models. Stochastic simulations verify that our results are robust to estimation error. |
| Keywords: | tennis, games, Nash equilibrium, Minimax theorem, constant sum games, mixed strategies, dynamic directional games, binary Markov games, dynamic programming, structural estimation, muscle memory, magnification effect |
| JEL: | C61 C73 L21 |
| Date: | 2023–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~23-23-03&r=gth |
| By: | Gisèle Umbhauer |
| Abstract: | In this second paper on the hammer-nail game, we confront strength with dexterity. The hammer-nail game, a game played in the French TV show “Fort Boyard”, goes as follows: two players are in front of a nail slightly driven into a wooden support. Both have a hammer and in turn hit the nail. The winner is the first player able to fully drive the nail into the support. A player is of strength f if he is able, with one swing of the hammer, to drive the nail at most f millimeters into the support. A player is of non dexterity e if he is unable to hammer smoothly, so that, with one swing of the hammer, he drives the nail at least e millimeters into the support, with \uD835\uDC52 > 1. In a previous paper, we mainly studied the impact of strength, both players being of high dexterity (\uD835\uDC52 = 1), and we transformed the hammer-nail game into a Nim game with incomplete information on strength. In this paper we study the impact of both strength and dexterity. We confront two players of different strength and dexterity and namely show a sad result: strength is more useful than dexterity to win the game. We also study the behavior in front of incomplete information, either on strength or on dexterity. |
| Keywords: | Nim game, crossed cycles, Fort Boyard, subgame perfect Nash equilibrium, strength, dexterity, incomplete information, heuristics of behavior. |
| JEL: | C72 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2023-31&r=gth |
| By: | Weihua Ruan (Purdue University Northwest, USA); Benteng Zou (DEM, Université du Luxembourg) |
| Abstract: | With the exhaustion of non-renewable resources and the increasing importance of criti- cal materials for the transition to clean technology, recycling is being called into action. Fulfilling demand for critical minerals involves challenges such as supply chain disruption, resource depletion and positive minimum demand, however. Under Markovian competi- tion between an exporting cartel and an importing country, we demonstrate that (i) if both virgin and recyclable resources are abundant, multiple subgame perfect Markovian Nash equilibria arise; (ii) if the exporting cartel can choose which Nash equilibrium to follow, when the cost of exploiting the non-renewable resource is sufficiently high, stopping the supply of virgin resource to the market is the Nash equilibrium; (iii) the consequence of this choice is that when the recyclable resource is exhausted, there is no Nash equilibrium anymore, although there remains virgin resource to exploit. |
| Keywords: | critical minerals, recycling, import and export, differential game, Hamilton-Jacobi-Bellman. |
| JEL: | Q34 C61 D4 L72 L12 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:23-04&r=gth |
| By: | Axel Anderson (Department of Economics, Georgetown University); Nikoloz Pkhakadze (ISET-Tbilisi State University) |
| Abstract: | This paper considers Bayesian persuasion between a sender and two receivers. The sender's payoff is a function of the receivers' beliefs on the binary payoff relevant state. All agents share a common prior about this state. But, we assume disagreement about a payoff irrelevant state, a binary variable that enters no utility functions. If the sender's payoff is differentiable and strictly monotone, then the sender never fully conceals. A convex payoff is insufficient for full revelation, but guarantees that every signal rules out two of the four states. We measure polarization by the sender's expectation of the absolute difference between the receivers posterior beliefs on the payoff relevant state, and solve for the maximum polarization across all message services. With linear payoff functions, the sender chooses a message service that achieves a significant fraction of this maximum. The sender's payoff is strictly increasing in the prior disagreement between the receivers. Given extreme prior disagreement between the receivers, we explicitly solve for the optimal message service when the sender has monotone payoffs in two general cases: bi-concave and bi-convex preferences. In both cases, the optimal message services induce polarization equal to the common prior on the sender's least preferred payoff relevant state. |
| Keywords: | Polarization, Endogenous Polarization, Communication Games, Bayesian Persuasion |
| JEL: | C72 |
| Date: | 2023–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~23-23-04&r=gth |
| By: | Manfred Kerber (University of Birmingham); Colin Rowat (University of Birmingham); Naoki Yoshihara (University of Massachusetts Amherst) |
| Abstract: | We study pillage games (Jordan in J Econ Theory 131.1:26–44, 2006, “Pillage and property†), which model unstructured power contests. To enable empirical tests of pillage game theory, we relax a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. We characterise the core for all n. In the three-agent game: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory. |
| Keywords: | power contests, core, stable sets |
| JEL: | C71 D51 P14 |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2023-3&r=gth |
| By: | Moez Kilani; André de Palma |
| Abstract: | We analyze spatial competition on a circle between firms that have multiple outlets and face quadratic transport costs. The equilibrium is a two-stage Nash game: first, firms decide on their locations and then set their prices. We are able to solve analytically simple multi-outlet cases, but for the general case, we require an algorithm to enumerate all non-isomorphic configurations. While price equilibria are explicit and unique, solving the full two-stage game requires numerical methods. In the location game, we consider two scenarios: either firms cannot jump one outlet over a competitors’ outlet, or firms have the flexibility to locate outlets anywhere on the circle. The solution involves a balance between cannibalization, market protection, and spatial monopoly power. We compare prices, profits, and transport costs for all possible configurations. With flexible locations, the firms’ market areas are contiguous. In this case, surprisingly, each firm acts as a spatial monopoly. If regulations enforce that each firm must set the same price for its outlets, head-to-head competition prevails, leading to decreased profits for the firms but to a better-off situation for consumers. |
| Keywords: | Spatial competition, circle, multi-product oligopoly, price-location equilibria, coin change problem. |
| JEL: | L13 R32 R53 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2023-33&r=gth |
| By: | Jenny S Kim; Kyungmin Kim; Richard Van Weelden |
| Abstract: | We consider the classic veto bargaining model but allow the agenda setter to engage in persuasion to convince the veto player to approve her proposal. We fully characterize the optimal proposal and experiment when Vetoer has quadratic loss, and show that the proposer-optimal can be achieved either by providing no information or with a simple binary experiment. Proposer chooses to reveal partial information when there is sufficient expected misalignment with Vetoer. In this case the opportunity to engage in persuasion strictly benefits Proposer and increases the scope to exercise agenda power. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.13148&r=gth |
| By: | Dirk Bergemann; Tan Gan; Yingkai Li |
| Abstract: | We study a sender-receiver model where the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the signal structure and the signal realization that the sender adopts. This framework captures applications where a decision-maker (the receiver) solicit advice from an interested party (sender). In these applications, the receiver faces uncertainty regarding the sender's preferences and the set of feasible signal structures. Consequently, we adopt a unified robust analysis framework that includes max-min utility, min-max regret, and min-max approximation ratio as special cases. We show that it is optimal for the receiver to sacrifice ex-post optimality to perfectly align the sender's incentive. The optimal decision rule is a quota rule, i.e., the decision rule maximizes the receiver's ex-ante payoff subject to the constraint that the marginal distribution over actions adheres to a consistent quota, regardless of the sender's chosen signal structure. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.10024&r=gth |
| By: | William Brock; Anastasios Xepapadeas |
| Abstract: | Scientific evidence suggests that anthropogenic impacts on the environment, such as land use changes and climate change, promote the emergence of infectious diseases (IDs) in humans. We develop a tworegion epidemic-economic model which unifies short-run disease containment policies with long-run policies which could control the drivers and the severity of IDs. We structure our paper by linking susceptible-infected-susceptible and susceptible-infected-recovered models with an economic model which includes land-use choices for agriculture and climate change and accumulation of knowledge that supports landaugmenting technical change. The contact number depends on shortrun containment policies (e.g., lockdown, vaccination), and long-run policies affecting land use, the natural world and climate change. Climate change and land-use change have an additional cost in terms of IDs since they might increase the contact number in the long run. We derive optimal short-run containment controls for a Nash equilibrium between regions, and long-run controls for climate policy, land use and knowledge at an open loop Nash equilibrium and the social optimum and unify the short- and long-run controls. We explore the impact of ambiguity aversion and model misspecification in the unified model and provide simulations which support the theoretical model. |
| Keywords: | infectious diseases, SIS and SIR models, natural world, climate change, land use, containment, Nash equilibrium, OLNE, social optimum, land-augmenting technical change |
| JEL: | I18 Q54 D81 |
| Date: | 2023–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:2319&r=gth |
| By: | Irebe Valsecchi (University of Milano-Bicocca) |
| Abstract: | For two periods an expert E announces his forecast of the state to a decision-maker D who chooses action. They disagree about the precision of the probability assessments. At the end of period 1 the state is observed. In the last period E makes announcements more extreme than his forecasts. Despite countable equilibria, full revelation is never realised. When in period 1 E is interested in reputation only, the initial equilibrium partition is finite; E makes announcements of greater uncertainty with respect to his forecasts. When E is interested in action too, reputational concerns mitigate exaggerated reports. |
| Keywords: | Cheap-talk, expert, statistical bias |
| JEL: | D81 D84 |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2023.20&r=gth |
| By: | Perrin Lefebvre (DeFiPP - Development Finance and Public Policies); David Martimort (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Lobbying competition is viewed as a delegated common agency game under moral hazard. Several interest groups try to influence a policy-maker who exerts effort to increase the probability that a reform be implemented. With no restriction on the space of contribution schedules, all equilibria perfectly reflect the principals' preferences over alternatives. As a result, lobbying competition reaches efficiency. Unfortunately, such equilibria require that the policy-maker pays an interest group when the latter is hurt by the reform. When payments remain non-negative, inducing effort requires leaving a moral hazard rent to the decision- maker. Contributions schedules no longer reflect the principals preferences, and the unique equilibrium is inefficient. Free-riding across congruent groups arises and the set of groups active at equilibrium is endogenously derived. Allocative efficiency and redistribution of the aggregate surplus are linked altogether and both depend on the set of active principals, as well as on the groups size. |
| Keywords: | Pluralistic Politics, Lobbying, Common Agency, Moral Hazard |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04234620&r=gth |
| By: | Yiwen Chen (Shandong Agricultural University, CH); Xi Wan (Nanjing Audit University, CH); Benteng Zou (DEM, Université du Luxembourg) |
| Abstract: | Carbon capture and storage (CCS) is considered one of the most important and efficient tools in fighting against greenhouse gas emissions. Countries differ in terms of the level CCS processes implemented, with the main barrier to CCS adoption being its high cost. This paper introduces a differential game model with heterogeneous countries to investigate the optimal timing for countries to initiate CCS projects, taking into account CCS costs. We show that (i) the thresholds for the triggering of CCS projects depend not only on one's own CCS costs but also those of others, in addition to the pollution damage costs; (ii) the optimal timing for different countries to initiate their CCS projects is the moment when their threshold level of pollution stock is reached; (iii) countries are more inclined to free-ride by both reducing pollutant emissions and deploying CCS when pollution damage costs are symmetric rather than asymmetric; finally, (iv) we provide sufficient conditions under which some countries never deploy CCS even though they bear the same pollution damage as the others. |
| Keywords: | Carbon capture and storage, optimal timing, Markovian perfect equilibrium. |
| JEL: | Q53 Q58 C61 C72 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:23-06&r=gth |
| By: | Michele Vodret |
| Abstract: | Time irreversibility in neuronal dynamics has recently been demonstrated to correlate with various indicators of cognitive effort in living systems. Using Landauer's principle, which posits that time-irreversible information processing consumes energy, we establish a thermodynamically consistent measure of cognitive energy cost associated with belief dynamics. We utilize this concept to analyze a two-armed bandit game, a standard decision-making framework under uncertainty, considering exploitation, finite memory, and concurrent allocation to both game options or arms. Through exploitative, prediction-error-based belief dynamics, the decision maker incurs a cognitive energy cost. Initially, we observe the rise of dissipative structures in the steady state of the belief space due to time-reversal symmetry breaking at intermediate exploitative levels. To delve deeper into the belief dynamics, we liken it to the behavior of an active particle subjected to state-dependent noise. This analogy enables us to relate emergent risk aversion to standard thermophoresis, connecting two apparently unrelated concepts. Finally, we numerically compute the time irreversibility of belief dynamics in the steady state, revealing a strong correlation between elevated - yet optimized - cognitive energy cost and optimal decision-making outcomes. This correlation suggests a mechanism for the evolution of living systems towards maximally out-of-equilibrium structures. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.15082&r=gth |
| By: | Anna Kerkhof (LMU Munich and ifo Institute for Economic Research); Johannes Münster (University of Cologne johannes.muenster@uni-koeln.de) |
| Abstract: | Media content is an important privately supplied public good. While it has been shown that contributions to a public good crowd out other contributions in many cases, the issue has not been thoroughly studied for media markets yet. We show that in a standard model of commercial media bias, qualities of media content are strategic complements, whereby investments into quality crowd in further investments and engage competitors in a race to the top. Therefore, financially strong public service media can mitigate commercial media bias: the content of commercial media can be more in line with the preferences of the audience and less advertiser-friendly in a dual (mixed public and commercial) media system than in a purely commercial media market. |
| Keywords: | commercial media bias, public service media, advertising, two-sided markets, supermodular games, strategic complements, public goods |
| JEL: | C70 H41 L13 L51 L82 |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:261&r=gth |
| By: | Gustavo Berganti\~nos; Juan D. Moreno-Ternero |
| Abstract: | We study the problem of sharing the revenues raised from subscriptions to music streaming platforms among content providers. We provide direct, axiomatic and game-theoretical foundations for two focal (and somewhat polar) methods widely used in practice: pro-rata and user-centric. The former rewards artists proportionally to their number of total streams. With the latter, each user's subscription fee is proportionally divided among the artists streamed by that user. We also provide foundations for a family of methods compromising among the previous two, which addresses the rising concern in the music industry to explore new streaming models that better align the interests of artists, fans and streaming services. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.11861&r=gth |
| By: | Tan Gan; Nicholas Wu |
| Abstract: | An informed seller designs a dynamic mechanism to sell an experience good. The seller has partial information about the product match, which affects the buyer's private consumption experience. We characterize equilibrium mechanisms of this dynamic informed principal problem. The belief gap between the informed seller and the uninformed buyer, coupled with the buyer's learning, gives rise to mechanisms that provide the skeptical buyer with limited access to the product and an option to upgrade if the buyer is swayed by a good experience. Depending on the seller's screening technology, this takes the form of free/discounted trials or tiered pricing, which are prevalent in digital markets. In contrast to static environments, having consumer data can reduce sellers' revenue in equilibrium, as they fine-tune the dynamic design with their data forecasting the buyer's learning process. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.00846&r=gth |
| By: | Matthew Embrey (Department of Economics, University of Sussex, BN1 9SL Falmer, United Kingdom); Christian Seel; J. Philipp Reiss |
| Abstract: | This paper experimentally investigates excessive risk taking in contest schemes by implementing a stopping task based on Seel and Strack (2013). In this stylized setting, managers with contest payoffs have an incentive to delay halting projects with a negative expectation, with the induced inefficiency being highest for a moderately negative drift. The experiment systematically varies the negative drift (between-subjects) and the payoff incentives (within-subject). We find evidence for excessive risk taking in all our treatment conditions, with the non-monotonicity at least as problematic as predicted. Contrary to the theoretical predictions, this aggregate pattern of behaviour is seen even without contest incentives. Further analysis suggests that many subjects display behaviour consistent with some intrinsic motivation for taking risk. This intrinsic motive and the strategic motive for excessive risk taking reinforce the non-monotonicity. The experiment uncovers a behavioural nuance where contest incentives crowd out an intrinsic inclination to gamble. |
| Keywords: | Contests, Relative performance pay, Risk-taking behaviour, Laboratory experiment |
| JEL: | C72 C92 D81 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:sus:susewp:0623&r=gth |
| By: | Sidartha Gordon; Chantal Marlats; Lucie Ménager (LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée - UP2 - Université Panthéon-Assas) |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03987473&r=gth |