A cognitive hierarchy model of behavior in the action commitment game

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861-898, 2004)-where players have different levels of reasoning-to Huck et al. (Games Econ Behav 38:240-264, 2002) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29-46, 1990) action commitment game-a duopoly with endogenous timing of entry. We show that, for an empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in (2002). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model.

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.

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.

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.

A model for the evolution of reinforcement learning in fluctuating games

Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

How to Model Heterogeneity in Costly Punishment: Insights from Responders' Response Times

We investigate what processes may underlie heterogeneity in social preferences. We address this question by examining participants' decisions and associated response times across 12 mini-ultimatum games. Using a finite mixture model and cross-validating its classification with a response time analysis, we identified four groups of responders: one group takes little to no account of the proposed split or the foregone allocation and swiftly accepts any positive offer; two groups process primarily the objective properties of the allocations (fairness and kindness) and need more time the more properties need to be examined; and a fourth group, which takes more time than the others, appears to take into account what they would have proposed had they been put in the role of the proposer. We discuss implications of this joint decision-response time analysis.