Iterated Prisoners Dilemma with limited attention

How attention scarcity effects the outcomes of a game? We present our findings on a version of the Iterated Prisoners Dilemma (IPD) game in which players can accept or refuse to play with their partner. We study the memory size effect on determining the right partner to interact with. We investigate the conditions under which the cooperators are more likely to be advantageous than the defectors. This work demonstrates that, in order to beat defection, players do not need a full memorization of each action of all opponents. There exists a critical attention capacity threshold to beat defectors. This threshold depends not only on the ratio of the defectors in the population but also on the attention allocation strategy of the players.Як дефiцит уваги впливає на результати гри? Ми представляємо нашi результати на прикладi гри Iтерована дилема в’язня (Iterated Prisoners Dilemma (IPD)), в якiй гравцi можуть погоджуватися чи вiдмовлятися грати зi своїм партнером. Ми вивчаємо вплив розмiру пам’ятi на визначення вiдповiдного партнера для взаємодiї. Ми дослiджуємо умови, при яких ймовiрнiше стати партнерами нiж перебiжчиками. Ця робота демонструє, що для перемоги над дезертирством гравцi не потребують повного запам’ятовування кожної дiї всiх опонентiв. Для того, щоб перемогти перебiжчикiв iснує критичний порiг здатностi уваги. Цей порiг залежить не тiльки вiд частки перебiжчикiв в популяцiї, але також вiд стратегiї розподiлу уваги гравцiв

Iterated Prisoners Dilemma with limited attention

How attention scarcity effects the outcomes of a game? We present our findings on a version of the Iterated Prisoners Dilemma (IPD) game in which players can accept or refuse to play with their partner. We study the memory size effect on determining the right partner to interact with. We investigate the conditions under which the cooperators are more likely to be advantageous than the defectors. This work demonstrates that, in order to beat defection, players do not need a full memorization of each action of all opponents. There exists a critical attention capacity threshold to beat defectors. This threshold depends not only on the ratio of the defectors in the population but also on the attention allocation strategy of the players.Comment: 8 pages, 3 figure

Using a theory of mind to find best responses to memory-one strategies

Memory-one strategies are a set of Iterated Prisoner's Dilemma strategies that have been praised for their mathematical tractability and performance against single opponents. This manuscript investigates best response memory-one strategies with a theory of mind for their opponents. The results add to the literature that has shown that extortionate play is not always optimal by showing that optimal play is often not extortionate. They also provide evidence that memory-one strategies suffer from their limited memory in multi agent interactions and can be out performed by optimised strategies with longer memory. We have developed a theory that has allowed to explore the entire space of memory-one strategies. The framework presented is suitable to study memory-one strategies in the Prisoner's Dilemma, but also in evolutionary processes such as the Moran process, Furthermore, results on the stability of defection in populations of memory-one strategies are also obtained

Quantum Games and Quantum Strategies

We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.Comment: 4 pages, 4 figures, typographic sign error in the definition of the operator J correcte

Transforming Power Relationships: Leadership, Risk, and Hope. IHS Political Science Series No. 135, May 2013

Chronic communal conflicts resemble the prisoner’s dilemma. Both communities prefer peace to war. But neither trusts the other, viewing the other’s gain as its own loss, so potentially shared interests often go unrealized. Achieving positive-sum outcomes from apparently zero-sum struggles requires a kind of riskembracing leadership. To succeed leaders must: a) see power relations as potentially positive-sum; b) strengthen negotiating adversaries instead of weakening them; and c) demonstrate hope for a positive future and take great personal risks to achieve it. Such leadership is exemplified by Nelson Mandela and F.W. de Klerk in the South African democratic transition. To illuminate the strategic dilemmas Mandela and de Klerk faced, we examine the work of Robert Axelrod, Thomas Schelling, and Josep Colomer, who highlight important dimensions of the problem but underplay the role of risk-embracing leadership. Finally we discuss leadership successes and failures in the Northern Ireland settlement and the Israeli-Palestinian conflict

The Topology of Conflict and Co-operation

The class of simultaneous 2x2 pure-strategy ordinal games (which include well-known games such as Prisoner’s Dilemma, Chicken and Stag Hunt) have received considerable attention, including complete classification schemes by amongst others Rapoport & Guyer (1978) and Robinson & Goforth (2005). This paper focuses on a particularly pertinent subset of these games, described as the ‘Co-operate-Defect’ (C-D) games, which are characterised by each player having a dominant preference for a particular strategy by the other player. These games are therefore relevant in a number of contexts, including arms race games and collective action problems. The C-D games may be efficiently classified by assigning each player one of six distinct types, a classification that cannot be naturally extended to the full class of 2x2 games. The six types and the resulting game forms are analysed, and the subclass of CD games are identified within a topological structure for the 2x2 games devised by Robinson & Goforth (2005).Conflict; co-operation; game theory; co-operate-defect games

Evolutionary stable strategies in networked games: the influence of topology

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability' to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context

Environmental dilemmas revisited: structural consequences from the angle of institutional ergonomics

The structure of a social dilemma lies behind many environmental problems. Mingling temporal aspects of resources with the structure of the social dilemma often leads to wrong conclusions. Therefore, it is worth analytically separating temporal aspects from structural aspects of the dilemma. This article concentrates solely on the structural aspects of the dilemma and the grades of complexity with respect to the number and stakes of the people involved, as well as the asymmetry of endowments and the salience of the optimal use of the resource in order to come close to the welfare optimum. Dilemmas with sufficient complexity are extremely vulnerable to individual defectors, and therefore institutions are necessary for the solution of the dilemma. Consequently, research in environmental psychology should not only target the individuals, but focus on institutional design with respect to (1) the structural diagnosis of environmental dilemmas; (2) methods that provide an insight into the structural problem of environmental dilemmas; (3) the impact of institutions on internalizing norms; and (4) the impact of structural knowledge about the dilemma of accepting institutions that help to solve the environmental dilemma. In analogy to software-ergonomics, psychology should initiate research in institutional ergonomics that helps to create addressee-friendly institutions.