|
on Game Theory |
| By: | Bary S. R. Pradelski; Bassel Tarbush |
| Abstract: | In a $\textit{satisficing equilibrium}$ each agent plays one of their $k$ best pure actions, but not necessarily their best action. We show that satisficing equilibria in which agents play only their best or second-best action exist in almost all games. In fact, in almost all games, there exist satisficing equilibria in which all but one agent best-respond and the remaining agent plays at least a second-best action. By contrast, more than one third of games possess no pure Nash equilibrium. In addition to providing static foundations for satisficing equilibria, we show that a parsimonious dynamic converges to satisficing equilibria in almost all games. We apply our results to market design and show that a mediator who can control a single agent can enforce stability in most games. Finally, we use our results to study the existence of $\epsilon$-equilibria. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.00832 |
| By: | Zhang Xu; Wei Zhao |
| Abstract: | Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction, only (strict) Nash Equilibrium (NE) is stochastically stable. Therefore, the tacit collusion is driven by failure to learn NE due to insufficient learning, instead of learning some strategies to sustain collusive outcomes. Second, we study how algorithms adapt to collusion in real simulations with insufficient learning. Extensive explorations in early stages and discount factors inflates the Q-value, which interrupts the sequential and alternative price undercut and leads to bilateral rebound. The process is iterated, making the price curves like Edgeworth cycles. When both exploration rate and Q-value decrease, algorithms may bilaterally rebound to relatively high common price level by coincidence, and then get stuck. Finally, we accommodate our reasoning to simulation outcomes in the literature, including optimistic initialization, market design and algorithm design. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.01147 |
| By: | Luca Anderlini (Department of Economics, Georgetown University); GaOn Kim (MIT Sloan School of Management) |
| Abstract: | We consider auctions with N+1 bidders. Of these, N are symmetric and N+1 is "sufficiently strong'' relative to the others. The auction is a "tournament'' in which the first N players bid to win the right to compete with N+1. The bids of the first N players are binding and the highest bidder proceeds to a second-price competition with N+1. When N+1's values converge in distribution to an atom above the upper end of the distribution of the N bidders and the rest of the distribution is drained away from low values sufficiently slowly, the auction's expected revenue is arbitrarily close to the one obtained in a Myerson (1981) optimal auction. The tournament design is "detail free'' in the sense that no specific knowledge of the distributions is needed in addition to the fact that bidder N+1 is stronger than the others as required. In particular, no additional information about the value of the atom is needed. This is important since mis-calibrating by a small amount an attempt to implement the optimal auction can lead to large losses in revenue. We provide an interpretation of these results as possibly providing guidelines to a seller on how to strategically "populate'' auctions with a single bidder even when only weaker bidders are available. |
| Keywords: | Strong Insider, Tournament Auction, Approximate Optimality |
| JEL: | C70 C72 C79 |
| Date: | 2024–09–17 |
| URL: | https://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~24-24-04 |
| By: | Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada |
| Abstract: | While the market design advocates the importance of good design to achieve desirable properties, experiments on coalition formation theory have shown fragility in proposed mechanisms to do so. We experimentally investigate the effectiveness of “structured” mechanisms that implement the Shapley value as an ex-ante equilibrium outcome with those of corresponding “semi-structured” bargaining procedures. We find a significantly higher frequency of the grand coalition formation and the higher efficiency in the semi-structured than in the structured procedure regardless of whether it is demand-based or offer-based. While significant differences in the resulting allocations are observed between the two structured procedures, little difference is observed between the two semi-structured procedures. Finally, possibility of free-form chat induces the equal division more frequently than without it. Our results suggest, when it comes to bargaining and coalition formation, not having various restrictions imposed by different mechanisms may lead to more desirable outcomes. |
| Date: | 2023–11 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1221r |
| By: | Christopher Graser (Harvard University); Takako Fujiwara-Greve (Keio University); Julian García (Monash University); Matthijs van Veelen (University of Amsterdam) |
| Abstract: | Repetition is a classic mechanism for the evolution of cooperation. The standard way to study repeated games is to assume that there is an exogenous probability with which every interaction is repeated. If it is sufficiently likely that interactions are repeated, then reciprocity and cooperation can evolve together in repeated prisoner’s dilemmas. Who individuals interact with can however also be under their control, or at least to some degree. If we change the standard model so that it allows for individuals to terminate the interaction with their current partner, and find someone else to play their prisoner’s dilemmas with, then this limits the effectiveness of disciplining each other within the partnership, as one can always leave to escape punishment. The option to leave can however also be used to get away from someone who is not cooperating, which also has a disciplining effect. We find that the net effect of introducing the option to leave on cooperation is positive; with the option to leave, the average amount of cooperation that evolves in simulations is substantially higher than without. One of the reasons for this increase in cooperation is that partner choice creates endogenous phenotypic assortment. The model thereby produces a good match with many forms of human cooperation in repeated set- tings, where we end up interacting, not only with random others that we cannot separate from, once matched, or with others that are genetically related to us, but also with partners that we choose to stay with, and that end up being similarly dependable not to defect on us as we are not to defect on them. |
| JEL: | C73 |
| Date: | 2024–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240038 |
| By: | Yiwen Chen (Shandong Agricutural University, CN); Nora Paulus (University of Luxembourg); Xi Wan (Nanjing University, CN); Benteng Zou (DEM, Université du Luxembourg) |
| Abstract: | Carbon capture and storage (CCS) can be considered as one of the key tools in the fight against climate change, providing a promising method to reduce human-generated CO2 emissions. Despite its potential, the high cost of CCS deployment leads to an uneven adoption across countries. This paper employs a differential game model with heterogeneous countries facing transboundary pollution to determine the optimal timing to initiate CCS projects, and delivers analytical results for the existence of Markov Perfect Equilibria and the numerical illustration. We show that: (1) The trigger threshold for CCS deployment depends not only on a country’s own costs, but also on the costs of other countries and the costs associated with pollution damage. (2) The optimal timing for different countries to initiate their CCS projects occurs when a country’s pollution level reaches a critical threshold. (3) Countries are more inclined to freeride on the pollution abatement efforts of others when the pollution damage costs are symmetric rather than asymmetric. (4) Finally, we provide sufficient conditions under which some countries refrain from engaging in CCS, despite facing the same pollution damage costs as others. |
| Keywords: | Carbon capture and storage, optimal timing, Markovian perfect equilibrium. |
| JEL: | Q53 Q58 C61 C72 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:luc:wpaper:24-07 |
| By: | Zhongjian Lin; Francis Vella |
| Abstract: | We address the estimation of endogenous treatment models with social interactions in both the treatment and outcome equations. We model the interactions between individuals in an internally consistent manner via a game theoretic approach based on discrete Bayesian games. This introduces a substantial computational burden in estimation which we address through a sequential version of the nested fixed point algorithm. We also provide some relevant treatment effects, and procedures for their estimation, which capture the impact on both the individual and the total sample. Our empirical application examines the impact of an individual's exercise frequency on her level of self-esteem. We find that an individual's exercise frequency is influenced by her expectation of her friends'. We also find that an individual's level of self-esteem is affected by her level of exercise and, at relatively lower levels of self-esteem, by the expectation of her friends' self-esteem. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.13971 |
| By: | Vincent Meisner; Pascal Pillath |
| Abstract: | We design the profit-maximizing mechanism to sell an excludable and non-rival good with network effects. Buyers have heterogeneous private values that depend on how many others also consume the good. We characterize an algorithm that implements the optimal allocation in dominant strategies. We apply our insights to digital content creation, and we are able to rationalize features seen in monetization schemes in this industry such as voluntary contributions, community subsidies, and exclusivity bids. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.15196 |
| By: | Hirose, Kosuke; Matsumura, Toshihiro |
| Abstract: | This study theoretically investigates energy-saving investment incentives in duopolies. First, we investigate a binary choice model in which each firm chooses whether to make an energy-saving investment and then they face Cournot competition. We focus on the incentive to become the leading firm by the investment, when the rival does not engage in this project. We find the private incentive to be insufficient for welfare (thereby requiring promotion through policies), if Pigouvian tax is imposed. However, this incentive can be excessive when the emission tax rate is lower than the Pigouvian level. Next, we investigate a model in which firms can choose energy-saving investment levels continuously. We find that the equilibrium investment can be (is not) excessive for welfare when the emission tax rate is lower than (equal to) the Pigouvian. These results suggest a risk of policy formation combining a low emission tax and subsidies for promoting energy-saving investments. |
| Keywords: | emission tax; investment subsidy; policy combination; energy-conservation; production substitution |
| JEL: | L13 Q38 Q58 |
| Date: | 2024–08–27 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121836 |
| By: | Pengyu Wei; Wei Wei |
| Abstract: | This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhibit decreasing impatience, including the hyperbolic discount function as a special case. By deriving the Bellman system that characterizes the equilibrium, we establish the framework for analyzing investment behaviors of agents subject to decreasing impatience. From an economic perspective, we demonstrates that decreasing impatience prompts early investment. From a technical standpoint, we warn that decreasing impatience can lead to the failure of the smooth pasting principle. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.01478 |
| By: | Chen, Xuyang |
| 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. |
| Keywords: | Corporate taxes, Global minimum tax, Profit shifting, SBIE, Tax competition |
| JEL: | F21 F23 H25 H73 H87 |
| Date: | 2024–08–30 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121893 |
| By: | Alexander Matros; Vladimir Smirnov; Andrew Wait |
| Abstract: | Steg (2022) notes that Smirnov and Wait (2021) holds only under an as- sumption of symmetry. Here we show that all the analysis for an asymmetric environment in Smirnov and Wait (2021) applies under the assumption that there is a positive trend in the local maxima of leader payo s. Moreover, this new assumption holds in all of the examples in the original paper, and is relevant in a broad range of economic scenarios. |
| Keywords: | timing games, second-mover advantage, preemption |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:syd:wpaper:2024-19 |