Evolution of reputation in networks: A mean field game approach

This work models the competitive behaviour of individuals who maximize their own utility managing their network of connections with other individuals. Utility is taken as a synonym of reputation in this model. Each agent has to decide between two variables: the quality of connections and the number of connections. Hence, the reputation of an individual is a function of the number and the quality of connections within the network. On the other hand, individuals incur in a cost when they improve their network of contacts. The initial value of the quality and number of connections of each individual is distributed according to an initial (given) distribution. The competition occurs over continuous time and among a continuum of agents. A mean field game approach is adopted to solve the model, leading to an optimal trajectory for the number and quality of connections for each individual.

Coalition formation in a contest game with three heterogeneous players

We analyze the incentives for cooperation of three players differing in their efficiency of effort in a contest game. We concentrate on the non-cooperative bargaining foundation of coalition formation, and therefore, we adopt a two-stage model. In the first stage, individuals form coalitions following a bargaining protocol similar to the one proposed by Gul (1989). Afterwards, coalitions play the contest game of Esteban and Ray (1999) within the resulting coalition structure of the first stage. We find that the grand coalition forms whenever the distribution of the bargaining power in the coalition formation game is equal to the distribution of the relative efficiency of effort. Finally, we use the case of equal bargaining power for all individuals to show that other types of coalition structures may be observed as well.

A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Coevolution of adaptive technology, maladaptive culture and population size in a producer-scrounger game.

Technology (i.e. tools, methods of cultivation and domestication, systems of construction and appropriation, machines) has increased the vital rates of humans, and is one of the defining features of the transition from Malthusian ecological stagnation to a potentially perpetual rising population growth. Maladaptations, on the other hand, encompass behaviours, customs and practices that decrease the vital rates of individuals. Technology and maladaptations are part of the total stock of culture carried by the individuals in a population. Here, we develop a quantitative model for the coevolution of cumulative adaptive technology and maladaptive culture in a 'producer-scrounger' game, which can also usefully be interpreted as an 'individual-social' learner interaction. Producers (individual learners) are assumed to invent new adaptations and maladaptations by trial-and-error learning, insight or deduction, and they pay the cost of innovation. Scroungers (social learners) are assumed to copy or imitate (cultural transmission) both the adaptations and maladaptations generated by producers. We show that the coevolutionary dynamics of producers and scroungers in the presence of cultural transmission can have a variety of effects on population carrying capacity. From stable polymorphism, where scroungers bring an advantage to the population (increase in carrying capacity), to periodic cycling, where scroungers decrease carrying capacity, we find that selection-driven cultural innovation and transmission may send a population on the path of indefinite growth or to extinction.

The Lottery Blotto Game

In this paper we relax the Colonel Blotto game assumption that for a given battle the player who allocates the higher measure of resources wins that battle. We assume that for a given battle, the Colonel who allocates the higher measure of resources is more likely to win that battle. We have a simpler model for which we are able to compute all Nash equilibria in pure strategies for any valuations pro le that players might have. Something that is not possible for the original Blotto game. JEL: C72, D74, H56. KEYWORDS: Colonel Blotto game; lottery contest function.

Cumulative cultural dynamics and the coevolution of cultural innovation and transmission: an ESS model for panmictic and structured populations.

When individuals in a population can acquire traits through learning, each individual may express a certain number of distinct cultural traits. These traits may have been either invented by the individual himself or acquired from others in the population. Here, we develop a game theoretic model for the accumulation of cultural traits through individual and social learning. We explore how the rates of innovation, decay, and transmission of cultural traits affect the evolutionary stable (ES) levels of individual and social learning and the number of cultural traits expressed by an individual when cultural dynamics are at a steady-state. We explore the evolution of these phenotypes in both panmictic and structured population settings. Our results suggest that in panmictic populations, the ES level of learning and number of traits tend to be independent of the social transmission rate of cultural traits and is mainly affected by the innovation and decay rates. By contrast, in structured populations, where interactions occur between relatives, the ES level of learning and the number of traits per individual can be increased (relative to the panmictic case) and may then markedly depend on the transmission rate of cultural traits. This suggests that kin selection may be one additional solution to Rogers's paradox of nonadaptive culture.

The credit ratings game

The spectacular failure of top-rated structured finance products has broughtrenewed attention to the conflicts of interest of Credit Rating Agencies (CRAs). We modelboth the CRA conflict of understating credit risk to attract more business, and the issuerconflict of purchasing only the most favorable ratings (issuer shopping), and examine theeffectiveness of a number of proposed regulatory solutions of CRAs. We find that CRAs aremore prone to inflate ratings when there is a larger fraction of naive investors in the marketwho take ratings at face value, or when CRA expected reputation costs are lower. To theextent that in booms the fraction of naive investors is higher, and the reputation risk forCRAs of getting caught understating credit risk is lower, our model predicts that CRAs aremore likely to understate credit risk in booms than in recessions. We also show that, due toissuer shopping, competition among CRAs in a duopoly is less efficient (conditional on thesame equilibrium CRA rating policy) than having a monopoly CRA, in terms of both totalex-ante surplus and investor surplus. Allowing tranching decreases total surplus further.We argue that regulatory intervention requiring upfront payments for rating services (beforeCRAs propose a rating to the issuer) combined with mandatory disclosure of any ratingproduced by CRAs can substantially mitigate the con.icts of interest of both CRAs andissuers.

An experimental study of adaptive behavior in an oligopolistic market game

We consider an oligopolistic market game, in which the players are competing firm in the same market of a homogeneous consumption good. The consumer side is represented by a fixed demand function. The firms decide how much to produce of a perishable consumption good, and they decide upon a number of information signals to be sent into the population in order to attract customers. Due to the minimal information provided, the players do not have a well--specified model of their environment. Our main objective is to characterize the adaptive behavior of the players in such a situation.

The credit ratings game

The collapse of so many AAA-rated structured finance products in 2007-2008has brought renewed attention to the causes of ratings failures and the conflicts of interestin the Credit Ratings Industry. We provide a model of competition among Credit RatingsAgencies (CRAs) in which there are three possible sources of conflicts: 1) the CRA conflictof interest of understating credit risk to attract more business; 2) the ability of issuersto purchase only the most favorable ratings; and 3) the trusting nature of some investorclienteles who may take ratings at face value. We show that when combined, these give riseto three fundamental equilibrium distortions. First, competition among CRAs can reducemarket efficiency, as competition facilitates ratings shopping by issuers. Second, CRAs aremore prone to inflate ratings in boom times, when there are more trusting investors, andwhen the risks of failure which could damage CRA reputation are lower. Third, the industrypractice of tranching of structured products distorts market efficiency as its role is to deceivetrusting investors. We argue that regulatory intervention requiring: i) upfront paymentsfor rating services (before CRAs propose a rating to the issuer), ii) mandatory disclosure ofany rating produced by CRAs, and iii) oversight of ratings methodology can substantiallymitigate ratings inflation and promote efficiency.

Social value orientation as a moral intuition: Decision-making in the dictator game

We studied the decision making process in the Dictator Game and showed that decisions are the result of a two-step process. In a first step, decision makers generate an automatic, intuitive proposal. Given sufficient motivation and cognitive resources, they adjust this in a second, more deliberated phase. In line with the social intuitionist model, we show that one s Social Value Orientation determines intuitive choice tendencies in the first step, and that this effect is mediated by the dictator s perceived interpersonal closeness with the receiver. Self-interested concerns subsequently leadto a reduction of donation size in step 2. Finally, we show that increasing interpersonal closeness can promote pro-social decision-making.

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

Mutual trust and cooperation in the evolutionary hawks-doves game

Using a new dynamical network model of society in which pairwise interactions are weighted according to mutual satisfaction, we show that cooperation is the norm in the hawks-doves game when individuals are allowed to break ties with undesirable neighbors and to make new acquaintances in their extended neighborhood. Moreover, cooperation is robust with respect to rather strong strategy perturbations. We also discuss the empirical structure of the emerging networks, and the reasons that allow cooperators to thrive in the population. Given the metaphorical importance of this game for social interaction, this is an encouraging positive result as standard theory for large mixing populations prescribes that a certain fraction of defectors must always exist at equilibrium.

Model development for capercaillie (Tetrao urogallus) habitat in the Jura Mountains (Western Switzerland)

Capercaillie, Tetrao urogallus, is a threatened species in central Europe, and Swiss populations declined 40 to 50 % between 1970 and 1985. Capercaillie are sensitive to forest structure, and loss of habitat is a major cause of their decline. Knowledge of habitat characteristics is therefore essential for capercaillie conservation. Here, we present models predicting capercaillie probability of occurrence, based on relevant structural habitat variables. Models were built using multiple logistic regression analyses on capercaillie presence/absence data. Vegetation survey was carried out in July 1999 in a 170-km2 forested area (Jura mountains, canton de Vaud, western Switzerland) inhabited by capercaillie and presence/absence of the species was assessed according to dropping presence/absence. The survey was based on 10-m-radius sample plots each in a 1-km2 forest patch (n = 76 with capercaillie droppings, n = 80 without). A first model included seven out of 27 measured habitat variables and a second model only four. The latter model best represents practical needs. It includes three variables which had a negative impact on capercaillie presence: tree and shrub covers and spruce, Picea excelsa, shrub cover, and one which had a positive effect: bilberry, Vaccinium myrtillus, cover, highlighting that capaercaillie selected open forest with high bilberry abundance. The model can be used to map potential capercaillie habitat distribution and to manage the habitat in favour of capercaillie (protection and adapted forestry practices) in the Swiss Jura mountains.