arXiv:2112.01693v1 [cs.GT] 3 Dec 2021 1 Optimism Brings Accurate Perception in Iterated Prisoner’s Dilemma Orhun G ¨ orkem and Haluk O. Bingol Abstract—We analyze an extended model of the Iterated Prisoner’s Dilemma where agents decide to play based on the data from their limited memory or on recommendation. The cooperators can decide whether to play with the matched opponent or not. The decisions of agents are directly linked to their optimism level since they decide to play if they believe the opponent has a high probability to cooperate. Optimism is precisely tuned by parameters named as optimism threshold and tolerance. Our experiment showed that being optimistic is better as it leads to more accurate judgments whereas acting pessimistic results in biased decisions. Index Terms—Complex networks, iterated prisoner’s dilemma, tolerance, optimism, Multi-agent systems, misjudgment, bias ✦ 1 I NTRODUCTION In the past, people used to live with their own relatives in small societies and present gradual introduction patterns. With the exponential population growth, large societies with frequent interactions between strangers appeared [1]. Then, with the enhancements in technology and the crucial place of world wide web in our lives, standards in human commu- nication improved. We can interact with people thousands of kilometers far from our location in a few seconds. This opportunity reduced the value of a single communication. People want to meet more people in shorter periods, and try to get as much information as possible soon. We as humans usually benefit from the power of this connectivity. For example, students and experts exchange information with like-minded people with the help of social media [2]. Yet, getting to know other people and evaluating their characteristics can be tricky especially with the rush in our era. It is a popular claim that people need to be careful about their interactions with strangers and should not trust them easily. In this work, we assert that being too skeptical can also be harmful against cooperation possibilities in Prisoner’s Dilemma game. Moreover, optimism can bring a more successful view of people to some extent. 2 BACKGROUND 2.1 Prisoner’s Dilemma Prisoner’s Dilemma is a simple game to evaluate the suc- cess of various game strategies by trying them against an opponent whose acts are unknown and unpredictable [3]. Two agents playing Prisoner’s dilemma are expected to choose between defecting and cooperating. According to their choices, they are awarded or punished. If an agent cooperates while the other defects, the cooperator gets the sucker payoff S and the defector gets the temptation payoff T . If both players choose to cooperate, then they both get the reward payoff R. In the case of mutual defection, both • O. G¨ orkem and H. O. Bingol are with Bogazici University. players get the punishment payoff P . In Prisoner’s Dilemma game, the payoffs should satisfy both S<P<R<T and S + T< 2R [3]. Cooperation is a costly sacrifice and surprisingly it sur- vived against mutation and selection in the nature [4] . For one round, it is always better to defect without regarding the act of the opponent agent if there is no specific modification as in The Expected Prisoner’s Dilemma [5] . However, in real life we come up against the consequences of our previous acts. Therefore, Iterated Prisoner’s Dilemma(IPD) is introduced. Iterated Prisoner’s Dilemma models are often used to explain sentient human behaviors [6]. In the model, agents play with each other consecutively and the result is determined according to the sum of consecutive rounds. Agents are able to remember their opponents’ previous decisions. Then they decide by taking the past rounds into account. This generally promotes the power of cooperation since P < R and reciprocal trust yields better results than reciprocal distrust. Yet, IPD with 2 people (2 IPD) is insufficient to represent most of the real-world problems [7]. Hence we use a system with N agents in our experiments. 2.2 IPDwRec Iterated Prisoner’s Dilemma with recommendation (IPDwRec) [8] is a model developed to simulate an environment, where agents play with each other in several combinations and make use of recommendations in their choices. We built our model over IPDwRec by appending some additional terms and procedures. 2.2.1 Population Iterated Prisoner’s Dilemma has some well-known strate- gies such as TitForTat, Grim, and Pavlov [9]. In these strategies, agents have the total control of their behaviors. However, IPDwRec is different. The population of IPDwRec consists of N self-interested agents [10]. Half of the agents are cooperators and the other half are defectors. Cooperation and defection are vulnerable to an error with rate of ǫ. Hence, a cooperator is expected to cooperate with proba- bility of 1 − ǫ and a defector is expected to cooperate with probability of ǫ.