Search Results (714)

We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk–dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection. Full article

In this article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines. Full article

In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments $e_i$, productivities $p_i$, and rewards $r_i$. 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 $e_i{p}_i$ can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher $e_i{p}_i$ are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity). Full article

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

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

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 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 $\frac{1}{4}$ 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 $R_y$ 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

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

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

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

A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk $\{X_n,n=0,1,\dots \}$ in the continuation region $C:=\{1,2,\dots \}$, and the second player seeks to maximize the survival time in C. The process starts at $X_0=x>0$ and the game ends the first time $X_n\le 0$. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly. Full article

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

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

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

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