The Evolution of Collaboration in Symmetric 2x2-Games with Imperfect Recognition of Types

A recent series of papers has introduced a fresh perspective on the problem of the evolution of human cooperation by suggesting an amendment to the concept of cooperation itself: instead of thinking of cooperation as playing a particular strategy in a given game, usually C in the prisoner's dilemma, we could also think of cooperation as collaboration, i.e. as coalitional strategy choice, such as jointly switching from (D;D) to (C;C). The present paper complements previous work on collaboration by expanding on its genericity while relaxing the assumption that collaborators are able to perfectly identify their own kind. Conditions for the evolutionary viability of such collaboration under fairly undemanding assumptions about population and interaction structure are derived. Doing so, this paper shows that collaboration is an adaptive principle of strategy choice in a broad range of niches, i.e., stochastic mixtures of games

Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable.

In this article, we analyze how reasonable it is to play according to some Nash equilibria if players have a preference for one of their opponents’ strategies. For this, we propose the concepts of collaborative dominance and collaborative equilibrium. First we prove that, when the collaborative equilibrium exists it is always efficient, what can be seen as a focal property. Further we argue that a reason for players choosing not to collaborate is if they are focusing in security instead of efficiency, in which case they would prefer to play maximin strategies. This argument allows us to reduce the hall of reasonable equilibria for games where a collaborative equilibrium exists. Finally, we point out that two-player zero-sum games do not have collaborative equilibrium and, moreover, if there exists a strategy profile formed only by collaboratively dominated actions it is a Nash equilibrium in such kind of game

Collaborative Dominance: When Doing Unto Others As You Would Have Them Do Unto You Is Reasonable.

In this article, we analyze how reasonable it is to play according to some Nash equilibria if players have a preference for one of their opponents’ strategies. For this, we propose the concepts of collaborative dominance and collaborative equilibrium. First we prove that, when the collaborative equilibrium exists it is always efficient, what can be seen as a focal property. Further we argue that a reason for players choosing not to collaborate is if they are focusing in security instead of efficiency, in which case they would prefer to play maximin strategies. This argument allows us to reduce the hall of reasonable equilibria for games where a collaborative equilibrium exists. Finally, we point out that two-player zero-sum games do not have collaborative equilibrium and, moreover, if there exists a strategy profile formed only by collaboratively dominated actions it is a Nash equilibrium in such kind of game

Competitive multi-player stochastic games with applications to multi-person financial contracts

Competitive Multi-Player Stochastic Games with Applications to Multi-Person Financial Contracts Ivan Guo Abstract In the financial market, almost all traded derivatives only involve two parties. The aim of this thesis is to design and evaluate financial contracts involving multiple parties. This is done by utilising and extending concepts from game theory, financial mathematics and backward stochastic differential equations. The thesis is divided into two parts: multi-player stochastic competitive games and multi-person financial contracts. The first part of the thesis proposes two novel classes of multi-period multi-player stopping games: the multi-player redistribution game and the multi-player affine game. Both formulations are generalisations of the classic two-player Dynkin game, with a focus on designing the dependence between the payoffs of all players and their stopping decisions. These games are shown to be weakly unilaterally competitive, and sufficient conditions are given for the existence of optimal equilibria (a new solution concept motivated by financial applications), individual values and coalition values. The second part of the thesis introduces the notion of multi-person financial contracts by extending the two-person game option. These contracts may involve an arbitrary number of parties and each party is allowed to make a wide array of decisions, which then determines the settlement date as well as the payoffs. The generalised Snell envelope is introduced for the valuation of multi-person contracts and sufficient conditions for the existence of unique and additive arbitrage prices are provided. Finally, a new class of multi-dimensional reflected backward stochastic differential equations are proposed to model multi-person affine game options under market friction

Competitive multi-player stochastic games with applications to multi-person financial contracts

Competitive Multi-Player Stochastic Games with Applications to Multi-Person Financial Contracts Ivan Guo Abstract In the financial market, almost all traded derivatives only involve two parties. The aim of this thesis is to design and evaluate financial contracts involving multiple parties. This is done by utilising and extending concepts from game theory, financial mathematics and backward stochastic differential equations. The thesis is divided into two parts: multi-player stochastic competitive games and multi-person financial contracts. The first part of the thesis proposes two novel classes of multi-period multi-player stopping games: the multi-player redistribution game and the multi-player affine game. Both formulations are generalisations of the classic two-player Dynkin game, with a focus on designing the dependence between the payoffs of all players and their stopping decisions. These games are shown to be weakly unilaterally competitive, and sufficient conditions are given for the existence of optimal equilibria (a new solution concept motivated by financial applications), individual values and coalition values. The second part of the thesis introduces the notion of multi-person financial contracts by extending the two-person game option. These contracts may involve an arbitrary number of parties and each party is allowed to make a wide array of decisions, which then determines the settlement date as well as the payoffs. The generalised Snell envelope is introduced for the valuation of multi-person contracts and sufficient conditions for the existence of unique and additive arbitrage prices are provided. Finally, a new class of multi-dimensional reflected backward stochastic differential equations are proposed to model multi-person affine game options under market friction

The role of side information in steganography

Das Ziel digitaler Steganographie ist es, eine geheime Kommunikation in digitalen Medien zu verstecken. Der übliche Ansatz ist es, die Nachricht in einem empirischen Trägermedium zu verstecken. In dieser Arbeit definieren wir den Begriff der Steganographischen Seiteninformation (SSI). Diese Definition umfasst alle wichtigen Eigenschaften von SSI. Wir begründen die Definition informationstheoretisch und erklären den Einsatz von SSI. Alle neueren steganographischen Algorithmen nutzen SSI um die Nachricht einzubetten. Wir entwickeln einen Angriff auf adaptive Steganographie und zeigen anhand von weit verbreiteten SSI-Varianten, dass unser Angriff funktioniert. Wir folgern, dass adaptive Steganographie spieltheoretisch beschrieben werden muss. Wir entwickeln ein spieltheoretisches Modell für solch ein System und berechnen die spieltheoretisch optimalen Strategien. Wir schlussfolgern, dass ein Steganograph diesen Strategien folgen sollte. Zudem entwickeln wir eine neue spieltheoretisch optimale Strategie zur Einbettung, die sogenannten Ausgleichseinbettungsstrategien.The  goal of digital steganography is to hide a secret communication in digital media. The common approach in steganography is to hide the secret messages in empirical cover objects. We are the first to define Steganographic Side Information (SSI). Our definition of SSI captures all relevant properties of SSI. We explain the common usage of SSI. All recent steganographic schemes use SSI to identify suitable areas fot the embedding change. We develop a targeted attack on four widely used variants of SSI, and show that our attack detects them almost perfectly. We argue that the steganographic competition must be framed with means of game theory. We present a game-theoretical framework that captures all relevant properties of such a steganographic system. We instantiate the framework with five different models and solve each of these models for game-theoretically optimal strategies. Inspired by our solutions, we give a new paradigm for secure adaptive steganography, the so-called equalizer embedding strategies

Strategic interaction and socio-economic structure

Gauer F. Strategic interaction and socio-economic structure. Bielefeld: Universität Bielefeld; 2016

Ellsberg games and the strategic use of ambiguity in normal and extensive form games

Sass L. Ellsberg games and the strategic use of ambiguity in normal and extensive form games. Bielefeld: Universität Bielefeld; 2013.In this thesis I propose a framework for normal and extensive form games where players can use Knightian uncertainty strategically. In such Ellsberg games, ambiguity-averse players may render their actions objectively ambiguous by using devices such as Ellsberg urns, in addition to the standard mixed strategies. This simple change in the foundations leads to a number of interesting phenomena. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes. This happens especially in games with an information structure in which a player has the possibility to threaten his opponents. I illustrate this with the example of a negotiation game with three players. This mediated peace negotiation does not have a Nash equilibrium with peace outcome, but does have a peace equilibrium when ambiguity is a possible strategy. That a game with more than two players can have interesting non-Nash Ellsberg equilibria is traced back to results on subjective equilibria. Ellsberg equilibria are mathematically characterized by the Principle of Indifference in Distributions. In an Ellsberg equilibrium, players are indifferent between all mixed strategies contained in the Ellsberg equilibrium strategy. Furthermore, I observe that in two-player games players can immunize against strategic ambiguity by playing their maximin strategy (if a completely mixed Nash equilibrium exists). I analyze Ellsberg equilibria in two-person games with common and conflicting interests. I provide a number of examples and general results how to determine the Ellsberg equilibria of these games. The equilibria of conflicting interest games (modified Matching Pennies) turn out to be consistent with experimental deviations from Nash equilibrium play. Finally, I define extensive form Ellsberg games. Under the assumption of dynamically consistent (rectangular) Ellsberg strategies, I prove a result analog to Kuhn’s theorem: rectangular Ellsberg strategies and Ellsberg behavior strategies are equivalent