# 经济代写|博弈论代写Game Theory代考|UTILIZATION OF AUTOMATA IN GAME THEORY

## 经济代写|博弈论代写Game Theory代考|The Utilization of Finite Automata in Game Theory

Finite Automata is one of the simplest types of automata that is used to represent the players’ behaviors in different games. In 2000, Dodis, et al. (2000) were the first who formalized the idea of finite automata in prisoner’s dilemma instead of modeling players as polynomially bounded Turing Machine.

The study presented in (Maenner, 2008) shows that infinitely repeated games, such as prisoner’s dilemma and Matching Pennies, have problems in learning and representing the strategies. Therefore, the study introduced dynamic systems where agents start the game with randomly chosen strategies which are represented by finite state automata. The agents are also allowed to change their strategies during the game.

The work presented by Bouhmala and Granmo (2010) shows the benefits of finite learning automata in helping agents to find the action that minimizes the expected number of penalties received, or maximizes the expected number of payoffs received.

According to Andreozzi, (2013), the author discusses the emergence of cooperation in repeated TrustMini games. The study focuses mainly on those games played by finite automaton in sequential game. Each state in the finite automaton is associated to a strategy, which is the strategy the automaton plays when in the state. The importance of this study is the result which shows that finite automaton plays an important role in representing the players’ behavior.

According to Faella, et al. (2014), the authors are interested in determining if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification in the context of verification of open systems and program synthesis. The research considers timed games, where the game graph is a timed automaton. The model presents an automata-theoretic approach to solve the addressed games. The core of this model is based on translating the timed automaton $\mathrm{A}$, and modeling the game graph into a tree automaton $\mathrm{A}^{\mathrm{T}}$ accepting all trees that correspond to a strategy of the protagonist. The results shows that the model can solve time games (e.g., Rabin and CTL) in exponential time.

El-Seidy (2015) studies the effect of noise on the degree of relatedness between the players, with respect to the behavior of strategies and its payoff. The model considers the repeated prisoners’ dilemma game, and any strategy represented by a finite two -state of automaton. With the assistance from finite automaton, the analysis showed that the noise has an impact on the performance of the players’ strategies with respect to some constant values.

The role of game theory as a formal tool for interacting entities is discusses in (Burkov \& Chaib-draa, 2015). The paper is approaching the complexity of computing equilibria in game theory through finite automata. They proposed a procedure which determines the strategy profiles as finite automata. The strategy profiles is implementing as automaton of a set of states $Q$ with initial state $q^0 \in Q$, a decision function $f=\left(f_i\right)_{i \in N}$, where $f_i: Q \mapsto \Delta\left(A_i\right)$ is the decision function of player $i$, and of a transition function $\tau$ : $Q \times A \mapsto Q$, which identifies the next state of the automaton. The analysis released that the proposed algorithm terminates in finite time and always return a non-empty subset of approximate subgame-perfect equilibria payoff profiles in any repeated games.

## 经济代写|博弈论代写Game Theory代考|The Utilization of Adaptive Automata in Game Theory

Adaptive automata-based models have been presented as powerful tools for defining complex languages. In order for adaptive automata to do self-modification, adaptive acts adhered to their state-transition rules are activated whenever the transition is used. Adaptive mechanism can be defined as adaptive actions which change the behavior of adaptive automata by modifying the set of rules defining it.

The work presented by Bertelle (2002) has focused on the models which can be used for simulating Prisoner’s Dilemma. The work showed how existing models and algorithms, in game theory, can be used with automata for representing the behaviors of players. The dynamical and adaptive properties can be described in term of specific operators based on genetic algorithms. In addition, the work showed that genetic operators on probabilistic automata enable the adaptive behavior to be modeled for prisoner dilemma strategies.

According to Ghnemat (2005), the author uses genetic algorithms to generate adaptive behaviors to be applied for modeling an adaptive strategy for the prisoner dilemma. They used adaptive automatabased model for the modeling agent behavior. According to Ghnemat et al.(2006), the researchers pay more attention to the iterated prisoner dilemma. An original evaluative probabilistic automaton was created for strategy modeling.

It has been shown that genetic automata are well-adapted to model adaptive strategies. As a result, we noticed that modeling the player behavior needs some adaptive attributes. However, the computable models related to genetic automata are good tools to model such adaptive strategy.

The work presented in Zhang (2009) has formed the collection of automata in a tree-like structure, and the modification of action possibility continued at different levels, according to the reward signs provided for all hierarchical levels.

Adaptive automata have computational power equivalent to a Turing Machine. Thus, strategies represented by adaptive automata may show more complex behaviors than the ones described by finite automata. For instance, learning mechanisms can be constructed using adaptive automata to represent adaptive learning mechanism based on specific input parameters.

However, finite automata are a particular case of adaptive automata. If the automata have no rules associating adaptive functions to transitions, the model can be reduced to finite automata. This characteristic is considered important to use adaptive automata naturally where finite automata are required.

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|The Utilization of Finite Automata in Game Theory

(Maenner, 2008) 中提出的研究表明，无限重复的游戏，例如囚徒困境和匹配便士，在学习和表示策略方面存在问题。因此，该研究引入了动态系统，在该系统中，代理人以随机选择的策略开始游戏，这些策略由有限状态自动机表示。代理人也可以在游戏过程中改变他们的策略。

Bouhmala 和 Granmo (2010) 提出的工作展示了有限学习自动机在帮助代理人找到最小化收到的预期惩罚数量或最大化收到的预期支付数量的操作方面的好处。

El-Seidy (2015) 研究了噪音对玩家之间相关程度的影响，涉及策略行为及其收益。该模型考虑了重复的囚徒困境博弈，以及由有限二态自动机表示的任何策略。在有限自动机的帮助下，分析表明噪声对玩家策略的性能有一定的影响。

## 经济代写|博弈论代写Game Theory代考|The Utilization of Adaptive Automata in Game Theory

Bertelle (2002) 提出的工作集中在可用于模拟囚徒困境的模型上。这项工作展示了博弈论中现有的模型和算法如何与自动机一起使用来表示玩家的行为。动态和自适应特性可以用基于遗传算法的特定算子来描述。此外，该工作表明，概率自动机上的遗传算子可以为囚徒困境策略建模适应性行为。

Zhang (2009) 提出的工作已经形成了树状结构的自动机集合，并且根据为所有层级提供的奖励标志，在不同层级继续修改动作可能性。

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