Search Results (13)

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

Clear cell renal cell carcinoma (CCRCC) is an aggressive form of cancer and a paradigmatic example of intratumor heterogeneity (ITH). The hawk-dove game is a mathematical tool designed to analyze competition in biological systems. Using this game, the study reported here analyzes the early phase of CCRCC development, comparing clonal fitness in homogeneous (linear evolutionary) and highly heterogeneous (branching evolutionary) models. Fitness in the analysis is a measure of tumor aggressiveness. The results show that the fittest clone in a heterogeneous environment is fitter than the clone in a homogeneous context in the early phases of tumor evolution. Early and late periods of tumor evolution in CCRCC are also compared. The study shows the convergence of mathematical, histological, and genomics studies with respect to clonal aggressiveness in different periods of the natural history of CCRCC. Such convergence highlights the importance of multidisciplinary approaches for obtaining a better understanding of the intricacies of cancer. Full article

A major challenge in cognitive science and AI has been to understand how intelligent autonomous agents might acquire and predict the behavioral and mental states of other agents in the course of complex social interactions. How does such an agent model the goals, beliefs, and actions of other agents it interacts with? What are the computational principles to model a Theory of Mind (ToM)? Deep learning approaches to address these questions fall short of a better understanding of the problem. In part, this is due to the black-box nature of deep networks, wherein computational mechanisms of ToM are not readily revealed. Here, we consider alternative hypotheses seeking to model how the brain might realize a ToM. In particular, we propose embodied and situated agent models based on distributed adaptive control theory to predict the actions of other agents in five different game-theoretic tasks (Harmony Game, Hawk-Dove, Stag Hunt, Prisoner’s Dilemma, and Battle of the Exes). Our multi-layer control models implement top-down predictions from adaptive to reactive layers of control and bottom-up error feedback from reactive to adaptive layers. We test cooperative and competitive strategies among seven different agent models (cooperative, greedy, tit-for-tat, reinforcement-based, rational, predictive, and internal agents). We show that, compared to pure reinforcement-based strategies, probabilistic learning agents modeled on rational, predictive, and internal phenotypes perform better in game-theoretic metrics across tasks. The outlined autonomous multi-agent models might capture systems-level processes underlying a ToM and suggest architectural principles of ToM from a control-theoretic perspective. Full article

Cultures around the world show varying levels of conservatism. While maintaining traditional ideas prevents wrong ones from being embraced, it also slows or prevents adaptation to new times. Without exploration there can be no improvement, but often this effort is wasted as it fails to produce better results, making it better to exploit the best known option. This tension is known as the exploration/exploitation issue, and it occurs at the individual and group levels, whenever decisions are made. As such, it is has been investigated across many disciplines. We extend previous work by approximating a continuum of traits under local exploration, employing the method of adaptive dynamics, and studying multiple fitness functions. In this work, we ask how nature would solve the exploration/exploitation issue, by allowing natural selection to operate on an exploration parameter in a variety of contexts, thinking of exploration as mutation in a trait space with a varying fitness function. Specifically, we study how exploration rates evolve by applying adaptive dynamics to the replicator-mutator equation, under two types of fitness functions. For the first, payoffs are accrued from playing a two-player, two-action symmetric game, we consider representatives of all games in this class, including the Prisoner’s Dilemma, Hawk-Dove, and Stag Hunt games, finding exploration rates often evolve downwards, but can also undergo neutral selection as well depending on the games parameters or initial conditions. Second, we study time dependent fitness with a function having a single oscillating peak. By increasing the period, we see a jump in the optimal exploration rate, which then decreases towards zero as the frequency of environmental change increases. These results establish several possible evolutionary scenarios for exploration rates, providing insight into many applications, including why we can see such diversity in rates of cultural change. Full article

The business cycle is a frequent topic in economic research; however, the approach based on individual strategies often remains neglected. The aspiration of this study is to prove that the behavior of individuals can originate and fuel an economic cycle. For this purpose, we are using an algorithm based on a repeated dove–hawk game. The results reveal that the sum of output in a society is affected by the ratio of individual strategies. Cyclical changes in this ratio will be translated into fluctuations of the total product of society. We present game theory modelling of a strategic behavioral approach as a valid theoretical foundation for explaining economic fluctuations. This article offers an unusual insight into the business cycle’s causes and growth theories. Full article

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences. Full article

Cooperation in social dilemmas plays a pivotal role in the formation of systems at all levels of complexity, from replicating molecules to multi-cellular organisms to human and animal societies. In spite of its ubiquity, the origin and stability of cooperation pose an evolutionary conundrum, since cooperation, though beneficial to others, is costly to the individual cooperator. Thus natural selection would be expected to favor selfish behavior in which individuals reap the benefits of cooperation without bearing the costs of cooperating themselves. Many proximate mechanisms have been proposed to account for the origin and maintenance of cooperation, including kin selection, direct reciprocity, indirect reciprocity, and evolution in structured populations. Despite the apparent diversity of these approaches they all share a unified underlying logic: namely, each mechanism results in assortative interactions in which individuals using the same strategy interact with a higher probability than they would at random. Here we study the evolution of cooperation in both discrete strategy and continuous strategy social dilemmas with assortative interactions. For the sake of tractability, assortativity is modeled by an individual interacting with another of the same type with probability r and interacting with a random individual in the population with probability $1-r$, where r is a parameter that characterizes the degree of assortativity in the system. For discrete strategy social dilemmas we use both a generalization of replicator dynamics and individual-based simulations to elucidate the donation, snowdrift, and sculling games with assortative interactions, and determine the analogs of Hamilton’s rule, which govern the evolution of cooperation in these games. For continuous strategy social dilemmas we employ both a generalization of deterministic adaptive dynamics and individual-based simulations to study the donation, snowdrift, and tragedy of the commons games, and determine the effect of assortativity on the emergence and stability of cooperation. Full article

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results. Full article

Implementing a land fallow policy is of great significance for ensuring China’s food security and promoting the improvement of the ecological environment. The implementation of a fallow project involves different stakeholders. Farmers are the main participants in the fallow project. The decision of farmers to practice fallow is the key factor for the successful development of the fallow project. Therefore, this study theoretically reveals the decision-making mechanism of farmers’ participation in cultivated land fallow by utilizing the hawk-dove evolutionary game theory among farmers and explains some challenges in the implementation of fallow in Guizhou Province. We drew the following conclusions: (1) The behavior of farmers will be affected by other farmers in the same situation, and the effects of mutual incentives and imitations between the groups of farmers are affected by their interests; (2) in the fallow project, the rate of choosing either fallow or unfallow depends on the ratio of fallow income to planting income. If the income of participating in fallow is higher, the demonstration effect of farmers participating in fallow is stronger, and the strategy of continued cultivation is adopted. The fewer unfallow farmers there are, the more consolidated the results of fallow will be; and (3) the government should protect the income of farmers after fallow as much as possible, implement flexible subsidy policies, and formulate corresponding policies to successfully consolidate the fallow results. Full article

This paper generalises the Hawk-Dove evolutionary game by introducing cost sharing ratios for both players, and applies the generalised Hawk-Dove model to conflict management in projects through investigating the stability of Nash equilibria. A model with clashing interests between a project owner and a contractor is considered to derive their strategy adaptation given the cost sharing ratios. As expected, the pure Nash equilibria are shown to be dominantly stable while the mixed strategy equilibrium is observed to be unstable, across the range of considered cost sharing ratios. In addition, simulations are conducted on the strategy adaptation and stability of the equilibria under noisy and latent conditions. The obtained results can be used by project managers in optimising their strategy in practice. Full article

Standard equilibrium concepts in game theory find it difficult to explain the empirical evidence from a large number of static games, including the prisoners’ dilemma game, the hawk-dove game, voting games, public goods games and oligopoly games. Under uncertainty about what others will do in one-shot games, evidence suggests that people often use evidential reasoning (ER), i.e., they assign diagnostic significance to their own actions in forming beliefs about the actions of other like-minded players. This is best viewed as a heuristic or bias relative to the standard approach. We provide a formal theoretical framework that incorporates ER into static games by proposing evidential games and the relevant solution concept: evidential equilibrium (EE). We derive the relation between a Nash equilibrium and an EE. We illustrate these concepts in the context of the prisoners’ dilemma game. Full article

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games. Full article

I study the speed of the evolutionary process on small heterogeneous graphs using the Hawk-Dove game. The graphs are based on empirical observation data of grooming interactions in 81 primate groups. Analytic results for the star graph have revealed that irregular graphs can slow down the evolutionary process by increasing the mean time to absorption. Here I show that the same effects can be found for graphs representing natural animal populations which are much less heterogeneous than star graphs. Degree variance has proven to be a good predictor for the mean time to absorption also for these graphs. Full article