scholarly journals Cooperation in the Prisoner’s Dilemma: an experimental comparison between pure and mixed strategies

2019 ◽  
Vol 6 (7) ◽  
pp. 182142
Author(s):  
Leonie Heuer ◽  
Andreas Orland
Keyword(s):  
Treatment Group ◽  
Prisoner's Dilemma ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Prisoner’S Dilemma ◽  
Experimental Comparison ◽  
Control Group ◽  
Strategy Group ◽  
Mixed Strategies ◽  
Pure Strategies

Cooperation is—despite not being predicted by game theory—a widely documented aspect of human behaviour in Prisoner’s Dilemma (PD) situations. This article presents a comparison between subjects restricted to playing pure strategies and subjects allowed to play mixed strategies in a one-shot symmetric PD laboratory experiment. Subjects interact with 10 other subjects and take their decisions all at once. Because subjects in the mixed-strategy treatment group are allowed to condition their level of cooperation more precisely on their beliefs about their counterparts’ level of cooperation, we predicted the cooperation rate in the mixed-strategy treatment group to be higher than in the pure-strategy control group. The results of our experiment reject our prediction: even after controlling for beliefs about the other subjects’ level of cooperation, we find that cooperation in the mixed-strategy group is lower than in the pure-strategy group. We also find, however, that subjects in the mixed-strategy group condition their cooperative behaviour more closely on their beliefs than in the pure-strategy group. In the mixed-strategy group, most subjects choose intermediate levels of cooperation.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

A Game Theory-Based Heuristic for the Two-Dimensional VLSI Global Routing Problem

2015 ◽  
Vol 24 (06) ◽  
pp. 1550082 ◽  
Author(s):  
Umair F. Siddiqi ◽  
Sadiq M. Sait ◽  
Yoichi Shiraishi
Keyword(s):  
Game Theory ◽  
Spanning Tree ◽  
Pure Strategy ◽  
Main Task ◽  
Mixed Strategies ◽  
Routing Problem ◽  
Pure Strategies ◽  
R Process ◽  
Valid Solution ◽  
Number Of Iterations

In this work we propose a game theory (GT)-based global router. It works in two steps: (i) Initial routing of all nets using maze routing with framing (MRF) and (ii) GT-based rip-up and reroute (R&R) process. In initial routing, the nets are divided into several small subsets which are routed concurrently using multithreading (MT). The main task of the GT-based R&R process is to eliminate congestion. Nets are considered as players and each player employs two pure strategies: (attempt to improve its spanning tree, and, do not attempt to improve its spanning tree). The nets also have mixed strategies whose values act as probabilities for them to select any particular pure strategy. The nets which select their first strategy will go through the R&R operation. We also propose an algorithm which computes the mixed strategies of nets. The advantage of using GT to select nets is that it reduces the number of nets and the number of iterations in the R&R process. The performance of the proposed global router was evaluated on ISPD'98 benchmarks and compared with two recent global routers, namely, Box Router 2.0 (configured for speed) and Side-winder. The results show that the proposed global router with MT has a shorter runtime to converge to a valid solution than that of Box Router 2.0. It also outperforms Side-winder in terms of routability. The experimental results demonstrated that GT is a valuable technique in reducing the runtime of global routers.

Conflict analysis based on the graph model for conflict resolution and grey matrix

2013 ◽  
Vol 3 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Xueshan Han ◽  
Thi Dieu Linh Nguyen ◽  
Haiyan Xu
Keyword(s):  
Conflict Resolution ◽  
Prisoner's Dilemma ◽  
Pure Strategy ◽  
Prisoner’S Dilemma ◽  
Graph Model ◽  
Conflict Analysis ◽  
Decision Makers ◽  
Analysis Model ◽  
Policy Makers ◽  
Content Type

PurposeThe purpose of this paper is to propose a complete theory of grey conflict analysis model based on grey game and the graph model for conflict resolution and also, to illustrate a case of “prisoner's dilemma” in the traditional grey game as an example.Design/methodology/approachBased on the theories of grey game and graph model for conflict resolution, this paper concentrates on the model of grey conflict analysis in a case of two players under the condition of symmetrical loss information. By analyzing decision makers, strategies, states, graph model and grey potential, and the number of decision makers' steps, the pure strategy Nash equilibrium is extended to grey potential‐general metarationality, grey potential‐symmetrical metarationality, and grey potential‐sequential stability. Meanwhile, the logical relationships between solutions are discussed. A specific case study is carried out to illustrate how the proposed grey conflict analysis model is used in practice.FindingsThe results in this paper indicate that more stable solutions are found when one considers the grey potential‐general metarationality, the grey potential‐symmetrical metarationality, and the grey potential‐sequential stability, and then solve the paradox of “prisoner's dilemma”.Practical implicationsThis new grey conflict analysis model could be used to provide useful information for policy makers during existing conflicts or negotiations among parties or enterprises.Originality/valueThe paper succeeds in constructing a new grey conflict analysis model, in which the solution concepts are studied; and the two‐player grey game will be extended to n‐players in the near future.

Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

1998 ◽  
Vol 01 (04) ◽  
pp. 325-359 ◽  
Author(s):  
Vivek S. Borkar ◽  
Sanjay Jain ◽  
Govindan Rangarajan
Keyword(s):  
Mixed Strategy ◽  
Replicator Dynamics ◽  
Pure Strategy ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Theoretic Model ◽  
Final States ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
Pure Strategies

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.

The effect of memory in prisoner’s dilemma game under multi-strategy update mechanism

2020 ◽  
Vol 31 (06) ◽  
pp. 2050077
Author(s):  
Hai Zhu ◽  
Zhen Wang ◽  
Qingyang Zhao ◽  
Xing Jin ◽  
Lanping Yu
Keyword(s):  
Prisoner's Dilemma ◽  
Mixed Strategy ◽  
Prisoner’S Dilemma ◽  
Joint Effect ◽  
Game Model ◽  
Prisoner’S Dilemma Game ◽  
Emergence Of Cooperation ◽  
Open Issue ◽  
Prisoner's Dilemma Game

Due to the heterogeneity of strategy updating rules progressively destroying the cluster of cooperators, cooperation would be heavily suppressed when players adopt mixed strategy updating rules. Thus, how to improve the emergence of cooperation with the scenario of heterogeneous strategy updating rules becomes an important open issue. In this paper, we introduce the memory factor into the game model, and then study the joint effect of memory and heterogeneous strategy updating rules on the emergence of cooperation. Detailly, in our game model, memory-based imitation and innovation are chosen as two different strategy updating rules. Afterwards, the annealing and quenching rules are specifically used as the methods to mix the proposed two memory-based strategy updating rules. At last, Monte Carlo simulations are conducted to demonstrate the significance of our model. The simulation results show that for memory-based imitators, memory is not always effective in promoting cooperation. It’s more like a catalyst. When the proportion of the memory-based imitation is large, it promotes the emergence of cooperation. When the proportion of innovation is large, it accelerates the extinction of cooperation; for overall proportion of cooperation, memory effectively promotes the emergence of cooperation and improves the ability of cooperators to resist high temptation, but memory is a partial optimization, it cannot offset the deterioration of cooperation caused by heterogeneous strategies updating rules, memory only reduces the degree of deterioration. Finally, compared with the annealing rule, the change of quenching rule is more smooth, because it is easier for cooperators to form clusters under the quenching rule. Our investigation sheds some light to the role of memory in prisoner’s dilemma game under heterogeneous strategies updating rules.

Sign in / Sign up

Export Citation Format

Share Document