International Game Theory Review, Ahead of Print. Why use a viabilistic approach to model economy? Because it is urgent to re-assess the modeling of the business cycle that integrates dynamic money creation and that has at its core the notion of constraints. The purpose of this paper is thus to propose an evolutionary economic model using a mathematical framework derived from set-valued analysis, differential inclusions and viability theory. As this approach is dynamical, the model will not use two concepts on which neo-classical economics are built i.e., (1) the existence of static repea ..read more

International Game Theory Review, Ahead of Print. Differential games with additive payoffs are considered. A new approach to constructing the characteristic function for such games is defined. Properties of optimality principles such as the core and the Shapley value constructed by applying the new characteristic function are studied. The solutions obtained are demonstrated by means of an example ..read more

International Game Theory Review, Ahead of Print. In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method in [Bensoussan, A., Huang, Z. and Yam, S. C. P. [2023] Control theory on Wasserstein space: A new approach to optimality conditions, Ann. Math. Sci. Appl.; Bensoussan, A., Tai, H. M. and Yam, S. C. P. [2023] Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations, preprint (2023), arXiv:2305.04019; Bensous ..read more

International Game Theory Review, Ahead of Print. Identifying a Subgame Perfect Nash Equilibrium (SPNE) of a two-player Stackelberg game could be not a manageable task, especially when the players have a continuum of actions and the follower’s best reply correspondence is not single-valued. Aim of the paper is to investigate the issue of construction of SPNEs in Stackelberg games by exploiting perturbations of both the action sets and the payoff functions of the leader and the follower. To achieve the goal, since the limit of SPNEs of perturbed games is not necessarily an SPNE of the original ..read more

International Game Theory Review, Ahead of Print. Zero-sum two-person finite undiscounted (limiting ratio average) semi-Markov games are considered where both the transition probabilities and the transition times are controlled by a fixed player in all states. We prove that, if such a game is unichain, the value and optimal stationary strategies of the players can be obtained from an optimal solution of the linear programming algorithm for the associated one player control stochastic game using a data transformation method. An example is provided for such class of games ..read more

International Game Theory Review, Ahead of Print. Terms like inducement, incentivization, persuasion, and to some extent enticement, are used in our daily lives to describe situations where one individual (decision maker, or entity) acts in a way to influence the decision-making process of another individual or individuals, where the outcome could benefit all involved or only the one who has initiated the process. Such influence could be exerted in two different ways (though variations do exist): via a direct input by the influencer into the utility or reward (or loss) of the receiving party ..read more

International Game Theory Review, Ahead of Print. In this paper, we consider a singular control optimization problem which generalizes the Gordon–Schaefer model. A population of individuals with endogenous growth is harvested by two independent agents, and their joint profit is maximized. We show that adding a second control to the standard model greatly complicates the standard solution, which is a Most Rapid Approach. We prove that no solution where both controls are singular can exist. Using numerical experiments, we exhibit situations where the optimal steady state corresponds to one of th ..read more

International Game Theory Review, Ahead of Print. It is well known that laboratory subjects often do not play mixed strategy equilibria games according to the theoretical predictions. However, little is known about the role of cognition in these strategic settings. We therefore conduct an experiment where subjects play a repeated hide and seek game against a computer opponent. Subjects play with either fewer available cognitive resources (high cognitive load treatment) or with more available cognitive resources (low cognitive load treatment). Surprisingly, we find some evidence that subjects i ..read more

International Game Theory Review, Ahead of Print. Game theory is of substantial significance in diverse domains, acting as a potent instrument to comprehend and assess strategic engagements among rational decision-makers. It formulates mathematical models to represent strategic interactions among rational decision-makers in the competitive world. Due to ambiguity in the real-world problems, acquiring the precise payoff values of a matrix game proves challenging. However, in numerous scenarios, these payoffs fluctuate within specific ranges, making them suitable for consideration as interval nu ..read more

International Game Theory Review, Ahead of Print. In this paper, we propose a novel approach to study the production of consumption goods within a price floor carbon emission trading scheme. A stochastic Stackelberg game is set up between the environment authority (Player 1), and the manufacturer/producer (Player 2). In such a hybrid emission trading scheme, the authority sets an emissions target and producers will choose to participate in carbon trading on this basis, subject to a stochastic demand with information delayed. When the stochastic demand is determined by the market sale price and ..read more