How Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma?

Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner’s Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. On the other hand, uncertainties, which may be caused by misperception, occur in IPD inevitably in practical circumstances. To better understand the situation, we consider the influence of misperception on ZD strategies in IPD, where the two players, player X and player Y , have different cognitions, but player X detects the misperception and it is believed to make ZD strategies by player Y. We provide a necessary and sufficient condition for the ZD strategies in IPD with misperception, where there is also a linear relationship between players’ utilities in player X’s cognition. Then we explore bounds of players’ expected utility deviation from a linear relationship in player X’s cognition with also improving its own utility.

Predicting human decision making in psychological tasks with recurrent neural networks

Unlike traditional time series, the action sequences of human decision making usually involve many cognitive processes such as beliefs, desires, intentions and theory of mind, i.e. what others are thinking. This makes predicting human decision making challenging to be treated agnostically to the underlying psychological mechanisms. We propose to use a recurrent neural network architecture based on long short-term memory networks (LSTM) to predict the time series of the actions taken by the human subjects at each step of their decision making, the first application of such methods in this research domain. In this study, we collate the human data from 8 published literature of the Iterated Prisoner's Dilemma comprising 168,386 individual decisions and postprocess them into 8,257 behavioral trajectories of 9 actions each for both players. Similarly, we collate 617 trajectories of 95 actions from 10 different published studies of Iowa Gambling Task experiments with healthy human subjects. We train our prediction networks on the behavioral data from these published psychological experiments of human decision making, and demonstrate a clear advantage over the state-of-the-art methods in predicting human decision making trajectories in both single-agent scenarios such as the Iowa Gambling Task and multi-agent scenarios such as the Iterated Prisoner's Dilemma. In the prediction, we observe that the weights of the top performers tends to have a wider distribution, and a bigger bias in the LSTM networks, which suggests possible interpretations for the distribution of strategies adopted by each group.

Collective Strategies With a Master-Slave Mechanism Dominate in Spatial-Iterated Prisoner's Dilemma

How cooperation emerges and persists in a population of selfish agents is a fundamental question in evolutionary game theory. The research shows that collective strategies with master-slave mechanism (CSMSM) defeat tit-for-tat and other well-known strategies in spatial iterated prisoner's dilemma. A CSMSM identifies kin members by means of a handshaking mechanism. If the opponent is identified as non-kin, a CSMSM will always defect. Once two CSMSMs meet, they play master and slave roles. A mater defects and a slave cooperates in order to maximize the master's payoff. CSMSM outperforms non-collective strategies in spatial IPD even if there is only a small cluster of CSMSMs in the population. The existence and performance of CSMSM in spatial iterated prisoner's dilemma suggests that cooperation first appears and persists in a group of collective agents.

Negotiations in the Iterated Prisoner’s Dilemma

William Press and Freeman Dyson’s 2012 results were new and unexpected, and still excite considerable response. Ethan Akin presents another approach to winning the iterated prisoner’s dilemma.

Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner’s Dilemma

Evolutionary game theory assumes that players replicate a highly scored player’s strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone’s strategy just by observing the behaviour. In this work, we consider players with memory-one stochastic strategies in the iterated Prisoner’s Dilemma, with an assumption that they cannot directly access each other’s strategy but only observe the actual moves for a certain number of rounds. Based on the observation, the observer has to infer the resident strategy in a Bayesian way and chooses his or her own strategy accordingly. By examining the best-response relations, we argue that players can escape from full defection into a cooperative equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner, provided that the cost of cooperation is low and the observational learning supplies sufficiently large uncertainty.

At Lunch with Freeman Dyson

This is the story of a minor discovery in mathematical game theory. It concerns the prisoner’s dilemma game, which, played once, involves little strategy. But consider the iterated prisoner’s dilemma (IPD) game. In the IPD, there is information in the previous plays, which each player can use to devise a superior strategy that remains self-interested.

Iterated Prisoner's Dilemma among mobile agents performing 2D random walk

When Iterated Prisoner's Dilemma takes place on a two-dimensional plane among mobile agents, the course of the game slightly differs from that one in a well-mixed population. In this paper we present a detailed derivation of the expected number of encounters required for Tit-for-tat strategy to get even with Always-Defect strategy in a Brownian-like population. It will be shown that in such an environment Tit-for-Tat can perform better than in a well-mixed population.