Landscape and flux for quantifying global stability and dynamics of game theory

Game theory has been widely applied to many areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux framework to quantify the global stability and global dynamics of the game theory. As an example, we investigated the models of three-strategy games: a special replicator-mutator game, the repeated prison dilemma model. In this model, one stable state, two stable states and limit cycle can emerge under different parameters. The repeated Prisoner's Dilemma system has Hopf bifurcation transitions from one stable state to limit cycle state, and then to another one stable state or two stable states, or vice versa. We explored the global stability of the repeated Prisoner's Dilemma system and the kinetic paths between the basins of attractor. The paths are irreversible due to the non-zero flux. One can explain the game for $Peace$ and $War$.Comment: 25 pages, 15 figure

Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games

We experimentally study the effect of asymmetry on cooperation in a 40 period prisoner's dilemma game in fixed partner design. We distinguish between a high and low payoff symmetric prisoner's dilemma and an asymmetric game combined out of both symmetric ones. Asymmetry significantly decreases cooperation, as low-type players are more likely to defect after mutual cooperation while high-type players initiate cooperation more often than the former. Asymmetry also has a significant negative effect on the stability of cooperation rendering long sequences of mutual cooperation extremely rare.Symmetry, Asymmetry, Prisoner's Dilemma, Experiments

MONETARY STABILITY VERSUS FINANCIAL STABILITY IN ADJUSTING THE REAL ECONOMY

Nowadays, in the economic theory and practice, there's commonly held idea that the primary objective of monetary policy should be price stability. However, the possibility of achieving this goal depends on the development and stability of the financial system. Even though financial stability represents a prerequisite for reaching the objective of price stability, the relationship manifests itself in reverse also. In the long term, the two objectives support and reinforce each other, but in the short term, there may occur certain incompatibilities, thus resulting in the central bank's dilemma of abandoning one in favor of the other. This paper aims to investigate precisely the circumstances in which the policies pursued to ensure price stability can cause or worsen financial stability.price stability, financial stability, central bank, monetary policy, National Bank of Romania

Evolution of Cooperation and Coordination in a Dynamically Networked Society

Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of acquaintances, we model the co-evolution of the agents' strategies and of the social network itself using two prototypical games, the Prisoner's Dilemma and the Stag Hunt. Allowing agents to dismiss ties and establish new ones, we find that cooperation and coordination can be achieved through the self-organization of the social network, a result that is non-trivial, especially in the Prisoner's Dilemma case. The evolution and stability of cooperation implies the condensation of agents exploiting particular game strategies into strong and stable clusters which are more densely connected, even in the more difficult case of the Prisoner's Dilemma.Comment: 18 pages, 14 figures. to appea

Rational Samaritans, Strategic Moves, and Rule-Governed Behavior: Some Remarks on James Buchanan's "Samaritan's Dilemma"

Using James Buchanan's "Samaritan's Dilemma" as a basic example, this paper analyses the problems that have to be solved if strategic behavior is necessary to escape from dilemma situations by changing the opponents' incentives. These problems are addressed within one-shot games as well as repeated games. Furthermore, the implications resulting from the assumption of common knowledge of rationality are analyzed. By using the concept of finite automata to model strategies for supergames, the possible relations with evolutionary game theory are spelled out. -- Dieser Beitrag untersucht am Beispiel von James Buchanans "Samariter-Dilemma" die Probleme, die es zu lösen gilt, wenn "strategisches Verhalten" im Sinne der Veränderung von Handlungsanreizen durch glaubhafte Drohungen und Versprechen notwendig ist, um Dilemmasituationen zu vermeiden. Dabei werden neben den grundelgenden Strukturen "Einmalspiel" und "Superspiel" auch die Besonderheiten der Annahme von "common knowledge" analysiert, und mit dem Konzept der als finite Automaten abbildbaren Superspielstrategien Brücken zur evolutorischen Spieltheorie geschlagen.rationality,altruism,evolutionary stability,strategic moves

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