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on Game Theory |
| By: | Mark Voorneveld |
| Abstract: | Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.11504 |
| By: | Dax Enshan Koh; Kaavya Kumar; Siong Thye Goh |
| Abstract: | The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a quantum variant of the classical volunteer's dilemma, generalizing it by allowing players to utilize quantum strategies. Employing the Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer quantum volunteer's dilemma scenario with an arbitrary number of players, where the cost of volunteering is shared equally among the volunteers. We derive analytical expressions for the players' expected payoffs and demonstrate the quantum game's advantage over the classical game. In particular, we prove that the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger expected payoffs compared to the unique symmetric Nash equilibrium of the classical game, wherein players use mixed strategies. Furthermore, we show that the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal distinct dynamics in volunteer's dilemma scenarios when players adhere to quantum rules, underscoring a strategic advantage of decision-making in quantum settings. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.05708 |
| By: | Marie Laclau; Péter Vida; Helmuts Azacis (CY Cergy Paris Université, THEMA) |
| Abstract: | We show that essentially every correlated equilibrium of any finite game with complete information with four players can be implemented as a perfect Bayesian equilibrium of an extended game, in which before choosing actions in the underlying game, players exchange cheap talk messages. In particular, we improve on the result of B´ar´any (1992) and Gerardi (2004). And our result generalizes to sequential equilibria and to games with incomplete information, i.e. to the set of (regular) communication equilibria. |
| Keywords: | nmediated communication; sequential rationality; correlated equilibria; communication equilibria; communication protocols |
| JEL: | C72 D82 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ema:worpap:2024-07 |
| By: | Pradeep Dubey; Siddhartha Sahi |
| Abstract: | Consider a noncooperative game at whose outcomes commodities accrue to players, which are both valued by them and susceptible to transfer between them. In this situation, outcome-contingent transfers of commodities form a natural schema for incentivizing cooperation, in the following sense. Transfers agreed upon by the players give rise to a new noncooperative game whose Nash Equilibria (NE) may engender a Pareto-improvement over some designated status quo NE of the original game. However, as in the folk theorem for repeated games, an embarrassingly large set of NE may be sustainable via transfers. The main source for this pathology is the possibility of “threats†, which can be understood as “off-shell†transfers, i.e. transfers at outcomes that are not actually being reached with positive probability at the NE under consideration. Our endeavor is to restore the discriminatory nature of NE by means of two simple ideas. We say that an NE of the post-transfers game is transparent if there are no off-shell transfers. This can also be viewed via the lens of “credibility†, of something being seen in order to be believed. The other condition is budget balance, i.e., at the NE, there should be no need for a net injection of commodities from the outside in order to sustain transfers. An NE is considered eligible by us if it satisfies these two conditions, in addition to engendering Pareto-improvement. If a social welfare function is specified, then one may seek to determine eligible NE that maximize welfare on the domain of feasible transfers. We carry out this analysis for three classical noncooperative games. These are the Centipede Game, Contest, and the Prisoners’ Dilemma; the last of which we discuss in some detail. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:nys:sunysb:24-03 |
| By: | Arthur B. Nelson; Dmitry Ryvkin |
| Abstract: | We study experimentally contests in which players make investment decisions sequentially, and information on prior investments is revealed between stages. Using a between-subject design, we consider all possible sequences in contests of three players and test two major comparative statics of the subgame-perfect Nash equilibrium: The positive effect of the number of stages on aggregate investment and earlier mover advantage. The former prediction is decidedly rejected, as we observe a reduction in aggregate investment when more sequential information disclosure stages are added to the contest. The evidence on earlier mover advantage is mixed but mostly does not support theory as well. Both predictions rely critically on large preemptive investment by first movers and accommodation by later movers, which does not materialize. Instead, later movers respond aggressively, and reciprocally, to first movers' investments, while first movers learn to accommodate those responses. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.06230 |
| By: | Liu, Tingjun (The University of Hong Kong); Bernhardt, Dan (University of Illinois & University of Warwick) |
| Abstract: | We consider a classical auction setting in which an asset/project is sold to buyers who privately receive signals about expected payoffs, and payoffs are more sensitive to the signal of the bidder who controls the asset. We show that a seller can increase revenues by sometimes allocating cash-flow rights and control to different bidders, e.g., with the highest bidder receiving cash flows and the second-highest receiving control. Separation reduces a bidder’s information rent, which depends on the importance of his private information for the value of his awarded cash flows. As project payoffs are most sensitive to the information of the bidder who controls the project, allocating cash flow to another bidder lowers bidders’ informational advantage. As a result, when signals are close, the seller can increase revenues by splitting rights between the top two bidders. |
| Keywords: | Control and cash flow rights ; separation of rights ; mechanism design ; interdependent valuations JEL Codes: D44 ; D82 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1516 |
| By: | Ahmadzadeh, Amirreza |
| Abstract: | This paper examines a principal-agent model that the princi-pal mandates actions and conducts costly inspections without transfers. The principal prefers lower actions, while the agent prefers higher ac-tions and has private information about his type. The agent is protected by ex-post participation and rejects any action below his private type. The principal faces a trade-off between mandating lower actions and the risk the the agent rejects actions and chooses his outside option. We analyze various levels of the principal’s commitment ability. If the principal can commit to both inspections and actions when no inspec-tion is performed, and if the principal’s fear of ruin is greater than the agent’s, then a deterministic inspection policy is optimal. Additionally, if the principal cannot commit to either inspections or actions, the highest equilibrium payoff does not involve non-deterministic inspec-tion strategies. Finally, if the inspection cost is low and the principal commits to inspecting whenever requested by the agent, the principal can achieve the payoff of the optimal deterministic inspection policy.. |
| Keywords: | Costly state verification; mechanism design; cheap talk; inspection, limited commitment, regulation. |
| JEL: | D82 D86 M48 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129712 |
| By: | Margherita Comola (Université Paris-Saclay (RITM), PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Marie Claire Villeval (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique, IZA - Forschungsinstitut zur Zukunft der Arbeit - Institute of Labor Economics) |
| Abstract: | We experimentally investigate how players with opposing views compete for influence through strategic targeting in networks. We varied the network structure, the relative influence of the opponent, and the heterogeneity of the nodes' initial opinions. Although most players adopted a best-response strategy based on their relative influence, we also observed behaviors deviating from this strategy, such as the tendency to target central nodes and avoid nodes targeted by the opponent. Targeting is also affected by affinity and opposition biases, the strength of which depends on the distribution of initial opinions. |
| Keywords: | Network, Influence, Targeting, Competition, Experiment |
| Date: | 2024–09–23 |
| URL: | https://d.repec.org/n?u=RePEc:hal:cesptp:hal-04706311 |
| By: | Jun He; Andrew L. Liu |
| Abstract: | The integration of distributed energy resources (DERs) into wholesale energy markets can greatly enhance grid flexibility, improve market efficiency, and contribute to a more sustainable energy future. As DERs -- such as solar PV panels and energy storage -- proliferate, effective mechanisms are needed to ensure that small prosumers can participate meaningfully in these markets. We study a wholesale market model featuring multiple DER aggregators, each controlling a portfolio of DER resources and bidding into the market on behalf of the DER asset owners. The key of our approach lies in recognizing the repeated nature of market interactions the ability of participants to learn and adapt over time. Specifically, Aggregators repeatedly interact with each other and with other suppliers in the wholesale market, collectively shaping wholesale electricity prices (aka the locational marginal prices (LMPs)). We model this multi-agent interaction using a mean-field game (MFG), which uses market information -- reflecting the average behavior of market participants -- to enable each aggregator to predict long-term LMP trends and make informed decisions. For each aggregator, because they control the DERs within their portfolio under certain contract structures, we employ a mean-field control (MFC) approach (as opposed to a MFG) to learn an optimal policy that maximizes the total rewards of the DERs under their management. We also propose a reinforcement learning (RL)-based method to help each agent learn optimal strategies within the MFG framework, enhancing their ability to adapt to market conditions and uncertainties. Numerical simulations show that LMPs quickly reach a steady state in the hybrid mean-field approach. Furthermore, our results demonstrate that the combination of energy storage and mean-field learning significantly reduces price volatility compared to scenarios without storage. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.00107 |
| By: | Xuyang Chen |
| Abstract: | This paper investigates how the OECD's global minimum tax (GMT) affects multinational enterprises (MNEs) behavior and countries' corporate taxes. We consider both profit shifting and capital investment responses of the MNE in a formal model of tax competition between asymmetric countries. The GMT reduces the true tax rate differential and benefits the large country, while the revenue effect is generally ambiguous for the small country. In the short run where tax rates are fixed, due to tax deduction of the substance-based income exclusion (SBIE), a higher minimum rate exerts investment incentives but also incurs a larger revenue loss for the small country. We show that under high (low) profit shifting costs the former (latter) effect dominates so that the small country's revenue increases (decreases). In the long run where countries can adjust tax rates, the GMT reshapes the tax game and the competition pattern. In contrast to the existing literature, we reveal that the minimum rate binds the small country only if it is low. With the rise of the GMT rate, countries will undercut the minimum to boost real investments and collect top-up taxes. For small market-size asymmetry and intermediate profit shifting cost, the revenue loss from the elimination of profit shifting may dominate the revenue gain from taxing the true profits generated by substantive activities, so that even a marginal GMT reform may harm the small country. Otherwise, it can raise the small country's tax revenue. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.05397 |
| By: | D’Annunzio, Anna; Russo, Antonio |
| Abstract: | We study transaction fees applied by marketplace platforms where sellers (e.g., app developers) adopt freemium pricing. An ad valorem transaction fee reduces quality distortions introduced by the price-discriminating seller, thereby increasing consumer surplus. Moreover, a small fee increases welfare, implying that the agency model may be socially preferable to integration between platform and seller. However, the platform may set the equilibrium fee above the socially optimal level. Providing devices needed to access the marketplace (e.g., phones) induces the platform to raise the fee, whereas providing a product that competes with the seller induces a lower fee. |
| JEL: | D4 D21 L11 H22 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129704 |
| By: | Lin William Cong; Xiaohong Huang; Siguang Li; Jian Ni |
| Abstract: | We revisit the relationship between firm competition and real efficiency in a novel setting with informational feedback from financial markets. Although intensified competition can decrease market concentration in production, it reduces the value of proprietary information (e.g., market prospects) for speculators and discourages information production and price discovery in financial markets. Therefore, competition generates non-monotonic welfare effects through two competing channels: market concentration and information production. When information reflected in stock prices is sufficiently valuable for production decisions, competition can harm both consumer welfare and real efficiency. Our results are robust under cross-asset trading and learning and highlight the importance of considering the interaction between product market and financial market in antitrust policy, e.g., concerning the regulation of horizontal mergers. |
| JEL: | D61 D83 G14 G34 G40 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32944 |