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Games, Volume 14, Issue 6 (December 2023) – 10 articles

Cover Story (view full-size image): This paper investigates optimal delegation mechanisms in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation mechanisms: full delegation, veto-based delegation, and communication (no delegation). Contrary to conventional one-dimensional conflict models, pandering incentives and bias counterbalance each other, resulting in a principal’s benefit from delegation not strictly decreasing with increased bias. Surprisingly, delegation to a biased agent can be advantageous in certain scenarios. This research sheds light on the complex dynamics of delegation mechanisms, offering insights into principal–agent relationships. View this paper
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13 pages, 1782 KiB  
Article
Cooperation and Coordination in Threshold Public Goods Games with Asymmetric Players
Games 2023, 14(6), 76; https://doi.org/10.3390/g14060076 - 17 Dec 2023
Cited by 1 | Viewed by 953
Abstract
In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium [...] Read more.
In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group’s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people’s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity). Full article
(This article belongs to the Special Issue Competition, Coordination, and Cooperation: Theory and Evidence)
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20 pages, 3917 KiB  
Article
Collaborative Cost Multi-Agent Decision-Making Algorithm with Factored-Value Monte Carlo Tree Search and Max-Plus
Games 2023, 14(6), 75; https://doi.org/10.3390/g14060075 - 17 Dec 2023
Viewed by 819
Abstract
In this paper, we describe the Factored Value MCTS Hybrid Cost-Max-Plus algorithm, a collection of decision-making algorithms (centralized, decentralized, and hybrid) for a multi-agent system in a collaborative setting that considers action costs. Our proposed algorithm is made up of two steps. In [...] Read more.
In this paper, we describe the Factored Value MCTS Hybrid Cost-Max-Plus algorithm, a collection of decision-making algorithms (centralized, decentralized, and hybrid) for a multi-agent system in a collaborative setting that considers action costs. Our proposed algorithm is made up of two steps. In the first step, each agent searches for the best individual actions with the lowest cost using the Monte Carlo Tree Search (MCTS) algorithm. Each agent’s most promising activities are chosen and presented to the team. The Hybrid Cost Max-Plus method is utilized for joint action selection in the second step. The Hybrid Cost Max-Plus algorithm improves the well-known centralized and distributed Max-Plus algorithm by incorporating the cost of actions in agent interactions. The Max-Plus algorithm employed the Coordination Graph framework, which exploits agent dependencies to decompose the global payoff function as the sum of local terms. In terms of the number of agents and their interactions, the suggested Factored Value MCTS-Hybrid Cost-Max-Plus method is online, anytime, distributed, and scalable. Our contribution competes with state-of-the-art methodologies and algorithms by leveraging the locality of agent interactions for planning and acting utilizing MCTS and Max-Plus algorithms. Full article
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52 pages, 1651 KiB  
Article
Generalized Hyperbolic Discounting in Security Games of Timing
Games 2023, 14(6), 74; https://doi.org/10.3390/g14060074 - 30 Nov 2023
Viewed by 825
Abstract
In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at [...] Read more.
In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at a constant rate. As this research area evolves, attempts to introduce more economically realistic models have led to the application of various forms of economic discounting to the contested resource. This paper investigates the application of a two-parameter economic discounting method, called generalized hyperbolic discounting, and characterizes the game’s Nash equilibrium conditions. We prove that for agents discounting such that accumulated value generated by the resource diverges, equilibrium conditions are identical to those of non-discounting agents. The methodology presented in this paper generalizes the findings of several other studies and may be of independent interest when applying economic discounting to other models. Full article
(This article belongs to the Special Issue Game Theory for Cybersecurity and Privacy)
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16 pages, 1469 KiB  
Article
Factors in Learning Dynamics Influencing Relative Strengths of Strategies in Poker Simulation
Games 2023, 14(6), 73; https://doi.org/10.3390/g14060073 - 29 Nov 2023
Viewed by 941
Abstract
Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue [...] Read more.
Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents. Full article
(This article belongs to the Section Applied Game Theory)
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20 pages, 1016 KiB  
Article
Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou
Games 2023, 14(6), 72; https://doi.org/10.3390/g14060072 - 20 Nov 2023
Viewed by 1041
Abstract
This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the [...] Read more.
This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action. Full article
(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)
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20 pages, 506 KiB  
Article
Countervailing Conflicts of Interest in Delegation Games
Games 2023, 14(6), 71; https://doi.org/10.3390/g14060071 - 16 Nov 2023
Viewed by 885
Abstract
In this paper, we investigate optimal delegation mechanisms in the presence of countervailing conflicts of interest in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation [...] Read more.
In this paper, we investigate optimal delegation mechanisms in the presence of countervailing conflicts of interest in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation mechanisms: full delegation, veto-based delegation, and communication (no delegation). Contrary to conventional one-dimensional conflict models, our findings reveal a non-monotonic relationship between pandering incentives and bias. These conflicts counterbalance each other, resulting in a principal’s benefit from delegation not strictly decreasing with increased bias. Surprisingly, delegation to a biased agent can be advantageous in certain scenarios. This research sheds light on the complex dynamics of delegation mechanisms when confronted with countervailing conflicts of interest, offering insights into decision-making in principal–agent relationships. Full article
(This article belongs to the Section Applied Game Theory)
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20 pages, 998 KiB  
Article
Location of Firms and Outsourcing
Games 2023, 14(6), 70; https://doi.org/10.3390/g14060070 - 31 Oct 2023
Viewed by 873
Abstract
We analyze the location of final goods producers under spatial competition with strategic input price determination by firm-specific input suppliers when the final goods producers undertake complete outsourcing or bi-sourcing. Under complete outsourcing, the final goods producers locate closer as the distance between [...] Read more.
We analyze the location of final goods producers under spatial competition with strategic input price determination by firm-specific input suppliers when the final goods producers undertake complete outsourcing or bi-sourcing. Under complete outsourcing, the final goods producers locate closer as the distance between the input suppliers decreases, but the distance between the final goods producers may increase or decrease with the transportation costs of the consumers and the transportation costs between the input suppliers and the final goods producers depending on the distance between the input suppliers. The possibility of bi-sourcing reduces the benefit from saving the transportation costs between the input suppliers and the final goods producers, and creates effects which are opposite to those under complete outsourcing. Thus, our results differ significantly from the extant literature considering either no strategic input price determination or strategic input price determination under competition in the input market. We also discuss the implications on the profits, consumer surplus and welfare, and the implications of endogenous location choice of the input suppliers. Full article
(This article belongs to the Special Issue Game Theory in Economics: Recent Advances in Spatial Competition)
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21 pages, 330 KiB  
Article
Vertical Relationships with Hidden Interactions
Games 2023, 14(6), 69; https://doi.org/10.3390/g14060069 - 31 Oct 2023
Viewed by 824
Abstract
In an agency model with adverse selection, we study how hidden interactions between agents affect the optimal contract. The principal employs two agents who learn their task environments through their involvement. The principal cannot observe the task environments. It is important to note [...] Read more.
In an agency model with adverse selection, we study how hidden interactions between agents affect the optimal contract. The principal employs two agents who learn their task environments through their involvement. The principal cannot observe the task environments. It is important to note that hidden interactions, such as acts of sabotage or help between the agents, have the potential to alter each other’s task environments. Our analysis encompasses two distinct organizational structures: competition and cooperation. Without hidden interactions, the competitive structure is optimal because the cooperative structure only provides the agents with more flexibility to collusively misrepresent their task environments. With hidden interactions, however, the cooperative structure induces the agents to help each other to improve the task environments while removing sabotaging incentives at no cost once collusion is deterred. As a result, the cooperative structure can be optimal in such a case. We discuss the link between production technology and organizational structure, finding that complementarity in production favors cooperative structures. Full article
(This article belongs to the Special Issue Industrial Organization and Organizational Economics)
10 pages, 365 KiB  
Communication
A Discrete-Time Homing Problem with Two Optimizers
Games 2023, 14(6), 68; https://doi.org/10.3390/g14060068 - 27 Oct 2023
Viewed by 924
Abstract
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,} in the continuation region [...] Read more.
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,} in the continuation region C:={1,2,}, and the second player seeks to maximize the survival time in C. The process starts at X0=x>0 and the game ends the first time Xn0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly. Full article
(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)
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22 pages, 340 KiB  
Article
On a Special Two-Person Dynamic Game
Games 2023, 14(6), 67; https://doi.org/10.3390/g14060067 - 24 Oct 2023
Viewed by 894
Abstract
The asymptotical properties of a special dynamic two-person game are examined under best-response dynamics in both discrete and continuos time scales. The direction of strategy changes by the players depend on the best responses to the strategies of the competitors and on their [...] Read more.
The asymptotical properties of a special dynamic two-person game are examined under best-response dynamics in both discrete and continuos time scales. The direction of strategy changes by the players depend on the best responses to the strategies of the competitors and on their own strategies. Conditions are given first for the local asymptotical stability of the equilibrium if instantaneous data are available to the players concerning all current strategies. Next, it is assumed that only delayed information is available about one or more strategies. In the discrete case, the presence of delays has an effect on only the order of the governing difference equations. Under continuous scales, several possibilities are considered: each player has a delay in the strategy of its competitor; player 1 has identical delays in both strategies; the players have identical delays in their own strategies; player 1 has different delays in both strategies; and the players have different delays in their own strategies. In all cases, it is assumed that the equilibrium is asymptotically stable without delays, and we examine how delays can make the equilibrium unstable. For small delays, the stability is preserved. In the cases of one-delay models, the critical value of the delay is determined when stability changes to instability. In the cases of two and three delays, the stability-switching curves are determined in the two-dimensional space of the delays, where stability becomes lost if the delay pair crosses this curve. The methodology is different for the one-, two-, and three-delay cases outlined in this paper. Full article
(This article belongs to the Special Issue Learning and Evolution in Games, 1st Edition)
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