Game Theory and International Environmental Cooperation

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.

Pairwise comparison dynamics for games with continuous strategy space

The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing studies so far have been limited to discrete strategy spaces with a small number of available actions. In many cases, however, the choices available to agents are better characterized by continuous spectra. This paper suggests a generalization of the replicator framework that allows to study the adaptive dynamics of Q-learning agents with continuous strategy spaces. Instead of probability vectors, agents strategies are now characterized by probability measures over continuous variables. As a result, the ordinary differential equations for the discrete case are replaced by a system of coupled integral--differential replicator equations that describe the mutual evolution of individual agent strategies. We derive a set of functional equations describing the steady state of the replicator dynamics, examine their solutions for several two-player games, and confirm our analytical results using simulations.

Weinstein and Yildiz (2007) have shown that in static games, only very weak predictions are robust to perturbations of higher order beliefs. These predictions are precisely those provided by interim correlated rationalizability (ICR). This negative result is obtained under the assumption that agents have no information on payoffs. This assumption is unnatural in many settings. It is therefore natural to ask whether Weinstein and Yildiz's results remain true under more general information structures. This paper characterizes the “robust predictions” in static and dynamic games, under arbitrary information structures. This characterization is provided by an extensive form solution concept: interim sequential rationalizability (ISR). In static games, ISR coincides with ICR and does not depend on the assumptions on agents' information. Hence the “no information” assumption entails no loss of generality in these settings. This is not the case in dynamic games, where ISR refines ICR and depends on the details of the information structure. In these settings, the robust predictions depend on the assumptions on agents' information. This reveals a hitherto neglected interaction between information and higher order uncertainty, raising novel questions of robustness.

In this paper, we introduce a class of games which we term demand allocation games that combines the characteristics of finite games such as congestion games and continuous games such as Cournot oligopolies. In a strategy profile each player may choose both an action out of a finite set and a non-negative demand out of a convex and compact interval. The utility of each player is assumed to depend solely on the action, the chosen demand, and the aggregated demand on the action chosen. We show that this general class of games possess a pure Nash equilibrium whenever the players' utility functions satisfy the assumptions negative externality, decreasing marginal returns and homogeneity. If one of the assumptions is violated, then a pure Nash equilibrium may fail to exist. We demonstrate the applicability of our results by giving several concrete examples of games that fit into our model.

Finite Dynamic Games with Discrete Strategy Space: A First Approach

Particle Swarm Optimization (PSO) successfully finds a solution as shown in various literatures. In some problems creating on discrete space, adjustment control-parameter may be difficult to modify a reach of optimum solution. The paper proposes an approach applying roulette wheel selection to PSO, which can help PSO escape from a local solution. This approach tested on both continuous and discrete space by finding solution of 12-numerical functions and an engineering-problem. The experiment result showed that the proposed technique can help PSO getting the best result both problem spaces, the performance improvement but also maintain easily to implementation.

This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and sufficient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payoff functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price auctions are provided. The conditions are also appropriate for ensuring that computer generated equilibrium solutions can be extended to continuous strategy spaces.

本文首先设计了一种博弈模型来描述重大公共活动的安保问题. 在此模型中, 安全部门 (以下简 称安保方) 与恐怖分子 (以下简称攻击方) 均具有连续的策略空间.在此博弈模型的均衡策略下, 即安 保方的最优策略下

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games.

The social brain hypothesis suggests that humans evolved larger brains and intelligence as adaptations to an increasingly complex social environment. We believe that social role division is a key factor in the evolution of social intelligence. To examine the the role of this factor, we extend Challet and Zhang’s Minority Game by adding a pre-decision communication stage and using a continuous strategy space instead of a binary one, and develop an evolutionary model based on this game. The evolutionary simulations demonstrate that the system alternates between two states: one with homogeneous social behavior and the other with heterogeneous behavior. We observe differentiation of social roles in the latter state: we find a “pivotal agent” that tends to adopt low-risk, low payoff strategies but determines which strategy will be in the minority and which in the majority, and we find “risk taker” that tend to adopt high-risk, high pay-off strategies. Using social sensitivity as a measure of social intelligence, we show that the level of social sensitivity correlates with the social roles, and is also a major factor in the mechanisms by which social roles switch.

Anxiety and Learning in Dynamic and Static Clock Game Experiments

Technical Note: Parameterised-Response Zero-Intelligence (PRZI) Traders

Because of the nature of high mobility and dynamic network topology, Intrusion Detection Systems (IDSs) in Vehicular Ad-hoc Networks (VANETs) face the challenge in balancing the accuracy and efficiency of detection. Two crucial problems are remained unsolved in existing studies: 1) how to perceive the environmental change in the perspective of an IDS? 2) how to make the IDS adaptive in different scenarios? In this paper, a self-adaptive scheme is proposed for IDSs in VANETs based on Bayesian game theory and Deep Q-learning Network (DQN). In the scheme, the interactions between an IDS and attackers are formulated as a dynamic intrusion detection game, in which the proposed scheme decides either to just adjust or to completely retrain the IDS. The Nash Equilibria (NE) of the game is derived to reveal how the optimal decision of the IDS depends on the detection performance and road conditions. Moreover, a DQN-Adjustment is proposed to realize the self-adaptation of the IDS in the dynamic game. Simulation results show that the IDS with the proposed self-adaptive scheme has better performance than other existing IDSs with higher detection rate as well as lower detection time and overhead.

The Brazilian Antitrust Law established the Administrative Council for Economic Defence (CADE) as the body responsible for investigating and imposing sanctions for acts that violate the economic order, as well as for supervising acts of economic concentration. The field of game theory is concerned with the actions of decision-makers who are aware that their decisions affect one another. The objective of the proposed article is to analyse the legal framework of the Leniency Programme implemented by Brazil's Administrative Council for Economic Defence (CADE) using the tools provided by game theory, in particular sequential games with perfect information. The methodology employed is classified as theoretical research, utilising the deductive method with the objective of enhancing the proposed theme. In order to achieve this, two game models will be developed. Initially, it was observed that the benefits offered by the current Brazilian leniency programme are insufficient to persuade a potential cartel member to propose a leniency agreement. Conversely, in a second step, the introduction of immunity for applicants from civil damages caused by the cartel resulted in the conclusion that the Brazilian antitrust leniency programme becomes an important tool for deterring and combating cartels. KEYWORDS: Antitrust Law. Cartel. Game theory. Leniency. Sequential games.