Games

12 pages, 738 KiB

Open AccessArticle

Centralized versus Decentralized Cleanup of River Water Pollution: An Application to the Ganges

by Amitrajeet A. Batabyal and Hamid Beladi

Games 2023, 14(5), 66; https://doi.org/10.3390/g14050066 - 7 Oct 2023

Cited by 3 | Viewed by 1610

We exploit the public good attributes of Ganges water pollution cleanup and theoretically analyze an aggregate economy of two cities—Kanpur and Varanasi—through which the Ganges flows. Our specific objective is to study whether water pollution cleanup in these two cities ought to be [...] Read more.

We exploit the public good attributes of Ganges water pollution cleanup and theoretically analyze an aggregate economy of two cities—Kanpur and Varanasi—through which the Ganges flows. Our specific objective is to study whether water pollution cleanup in these two cities ought to be provided in a centralized or in a decentralized manner. We first determine the efficient cleanup amounts that maximize the aggregate surplus from making the Ganges cleaner in the two cities. Second, we compute the optimal amount of water pollution cleanup in the two cities in a decentralized regime in which spending on cleanup is financed by a uniform tax on the city residents. Third, we ascertain the optimal amount of water pollution cleanup in the two cities in a centralized regime subject to equal provision of cleanup and cost sharing. Fourth, we show that if the two cities have the same preference for pollution cleanup, then centralization is preferable to decentralization as long as there is a spillover from pollution cleanup. Finally, we show that if the two cities have dissimilar preferences for pollution cleanup, then centralization is preferable to decentralization as long as the spillover exceeds a certain threshold. Full article

(This article belongs to the Section Applied Game Theory)

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15 pages, 295 KiB

Open AccessArticle

When Efficiency Requires Arbitrary Discrimination: Theoretical and Experimental Analysis of Equilibrium Selection

by Werner Güth and Hironori Otsubo

Games 2023, 14(5), 65; https://doi.org/10.3390/g14050065 - 30 Sep 2023

Viewed by 1389

Abstract

Institutions may rely on fundamental principles, e.g., of legal philosophy, but may also have evolved according to institutional fitness, as gauged by a society’s well-being. In our stylized framework where two fundamental principles, equality and efficiency, conflict with each other, one of the [...] Read more.

Institutions may rely on fundamental principles, e.g., of legal philosophy, but may also have evolved according to institutional fitness, as gauged by a society’s well-being. In our stylized framework where two fundamental principles, equality and efficiency, conflict with each other, one of the three players is the third party who faces two symmetric co-players as culprits and determines whether to sanction the two culprits discriminatorily or treat them with parity. Relying on the theory of equilibrium selection, we derived equilibrium solutions and experimentally tested our behavioral hypotheses. We found that asymmetry in wealth between the two culprits let the sanctioning agent hold the richer culprit more responsible. Furthermore, our results demonstrated that when the sanctioning agent’s decision was observable, sanctioning the two culprits discriminatorily induced them to coordinate on an efficient outcome. Full article

(This article belongs to the Special Issue Fairness in Non-cooperative Strategic Interactions)

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19 pages, 356 KiB

Open AccessArticle

Game Theoretic Foundations of the Gately Power Measure for Directed Networks

by Robert P. Gilles and Lina Mallozzi

Games 2023, 14(5), 64; https://doi.org/10.3390/g14050064 - 26 Sep 2023

Viewed by 1371

Abstract

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can [...] Read more.

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the

β

-measure, and construct an axiomatisation of the Gately measure. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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25 pages, 426 KiB

Open AccessArticle

A Game-Theoretic Analysis of Baccara Chemin de Fer, II

by Stewart N. Ethier and Jiyeon Lee

Games 2023, 14(5), 63; https://doi.org/10.3390/g14050063 - 25 Sep 2023

Viewed by 1626

Abstract

In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a

2 \times 2^{484}

matrix game) and Model B3 (a

2^{5} \times 2^{484}

matrix game), both of which depend on [...] Read more.

In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a

2 \times 2^{484}

matrix game) and Model B3 (a

2^{5} \times 2^{484}

matrix game), both of which depend on a positive-integer parameter d, the number of decks. The key to solving the game under Model B2 was what we called Foster’s algorithm, which applies to additive

2 \times 2^{n}

matrix games. Here “additive” means that the payoffs are additive in the n binary choices that comprise a player II pure strategy. In the present paper, we consider analogous models of the casino game baccara chemin de fer that take into account the

100 α

percent commission on Banker (player II) wins, where

0 \leq α \leq 1 / 10

. Thus, the game now depends not just on the discrete parameter d but also on a continuous parameter

α

. Moreover, the game is no longer zero sum. To find all Nash equilibria under Model B2, we generalize Foster’s algorithm to additive

2 \times 2^{n}

bimatrix games. We find that, with rare exceptions, the Nash equilibrium is unique. We also obtain a Nash equilibrium under Model B3, based on Model B2 results, but here we are unable to prove uniqueness. Full article

(This article belongs to the Section Algorithmic and Computational Game Theory)

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12 pages, 274 KiB

Open AccessArticle

On the Nash Equilibria of a Duel with Terminal Payoffs

by Athanasios Kehagias

Games 2023, 14(5), 62; https://doi.org/10.3390/g14050062 - 21 Sep 2023

Viewed by 1211

Abstract

We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players

P_{1}, P_{2}

are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If

P_{n}

[...] Read more.

We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players

P_{1}, P_{2}

are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If

P_{n}

shoots

P_{m}

(

m \neq n

), either they hit and kill them (with probability

p_{n}

) or they miss and

P_{m}

is unaffected (with probability

1 - p_{n}

). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “cooperative” (i.e., non-shooting) non-stationary equilibria. We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma. Full article

(This article belongs to the Special Issue Learning and Evolution in Games, 1st Edition)

27 pages, 504 KiB

Open AccessArticle

A Two-Player Resource-Sharing Game with Asymmetric Information

by Mevan Wijewardena and Michael J. Neely

Games 2023, 14(5), 61; https://doi.org/10.3390/g14050061 - 17 Sep 2023

Viewed by 1419

Abstract

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each [...] Read more.

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an

ϵ

-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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8 pages, 299 KiB

Open AccessArticle

Delay to Deal: Bargaining with Indivisibility and Round-Dependent Transfer

by Jijian Fan

Games 2023, 14(5), 60; https://doi.org/10.3390/g14050060 - 13 Sep 2023

Viewed by 1219

Abstract

We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the [...] Read more.

We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the initial transfer is large enough, the subgame perfect Nash equilibrium consists of a finite number of rounds of delay before an agreement is reached. The equilibrium delay is longer when the players are more patient, and when the transfer is initially higher and depreciates slower. Nevertheless, the game’s chaotic characteristic makes it arduous to forecast the exact number of delayed rounds or which player will make the ultimate decision. This game can be applied to many social scenarios, particularly those with exogenous costs. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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16 pages, 5866 KiB

Open AccessArticle

The Art of Sharing Resources: How to Distribute Water during a Drought Period

by Sebastian Cano-Berlanga, María-José Solís-Baltodano and Cori Vilella

Games 2023, 14(5), 59; https://doi.org/10.3390/g14050059 - 25 Aug 2023

Viewed by 1434

Abstract

Water scarcity is a growing problem in many regions worldwide. According to the United Nations, around one-fifth of the world’s population lives in areas where water is scarce. Another one-quarter of the world’s population has to face water supply cuts, mainly because this [...] Read more.

Water scarcity is a growing problem in many regions worldwide. According to the United Nations, around one-fifth of the world’s population lives in areas where water is scarce. Another one-quarter of the world’s population has to face water supply cuts, mainly because this proportion of the population lacks the necessary infrastructure to acquire water from rivers and aquifers (UN, 2005). Water is a resource that is essential to human survival and is also present in all productive processes in the economy. Therefore, we are challenged to adequately manage water to ensure the population’s well-being and to achieve socioeconomic development. Specifically, this paper analyzes the situation present in the summer of 2022 at Riudecanyes (a village in Catalonia, Spain), where a drought problem exists. We propose applying the conflicting claims problem theory to give possible solutions to distribute the water. We propose to use this theory to describe the distribution of the available irrigation hours in 2022, considering the demand made by the farmers in the previous year, when there was regular irrigation. Full article

(This article belongs to the Special Issue Game Theory with Applications to Economics)

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19 pages, 706 KiB

Open AccessArticle

Border Games: A Game Theoretic Model of Undocumented Immigration

by Julide Yazar and Robert J. Gitter

Games 2023, 14(5), 58; https://doi.org/10.3390/g14050058 - 24 Aug 2023

Viewed by 1858

Abstract

We consider a game-theoretic model of undocumented immigration with the aim of emphasizing the strategic interaction between the different forces affecting the issue. Specifically, we analyze the strategic interaction between firms in the destination country, native labor, the elected officials in the destination [...] Read more.

We consider a game-theoretic model of undocumented immigration with the aim of emphasizing the strategic interaction between the different forces affecting the issue. Specifically, we analyze the strategic interaction between firms in the destination country, native labor, the elected officials in the destination country, and the undocumented immigrants from the Source Country. We show that the impact of border enforcement is dampened because strategic interaction between the players will tend to mute any unilateral changes. We also study the effect of uncertainty in the labor market on migration issues and analyze the two cases where policymakers have to make their decisions before (ex-ante) or after (ex-post) the market state is realized. Full article

(This article belongs to the Special Issue Game Theory Applications to Socio-Environmental Studies, Development Economics and Sustainability Research)

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Games, Volume 14, Issue 5 (October 2023) – 9 articles

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