Reasoning about strategies and rational play in dynamic games

We discuss a number of conceptual issues that arise in attempting to capture, in dynamic games, the notion that there is "common understanding" among the players that they are all rational.Belief revision, common belief, counterfactual, dynamic game, model of a game, rationality

The neural basis of bounded rational behavior

Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting – the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. We apply a cognitive hierarchy model to classify subject’s choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. We found a correlation between levels of strategic reasoning and activity in a neural network related to mentalizing, i.e. the ability to think about other’s thoughts and mental states. Moreover, brain data showed how complex cognitive processes subserve the higher level of reasoning about others. We describe how a cognitive hierarchy model fits both behavioural and brain data.Game theory, Bounded rationality, Neuroeconomics

GECKA3D: A 3D Game Engine for Commonsense Knowledge Acquisition

Commonsense knowledge representation and reasoning is key for tasks such as artificial intelligence and natural language understanding. Since commonsense consists of information that humans take for granted, gathering it is an extremely difficult task. In this paper, we introduce a novel 3D game engine for commonsense knowledge acquisition (GECKA3D) which aims to collect commonsense from game designers through the development of serious games. GECKA3D integrates the potential of serious games and games with a purpose. This provides a platform for the acquisition of re-usable and multi-purpose knowledge, and also enables the development of games that can provide entertainment value and teach players something meaningful about the actual world they live in

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs – up to level li – about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash (li; l-i)-equilibria capture players’ inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustrate the constructions.Incomplete-information games, high-order reasoning, type space, quotient space, hierarchies of beliefs, bounded rationality

Measuring Agents' Reaction to Private and Public Information in Games with Strategic Complementarities

In games with strategic complementarities, public information about the state of the world has a larger impact on equilibrium actions than private information of the same precision, because the former is more informative about the likely behavior of others. This may lead to welfare-reducing ‘overreactions’ to public signals. We present an experiment based on a game of Morris and Shin (2002), in which agents’ optimal actions are a weighted average of the fundamental state and their expectations of other agents’ actions. We measure the responses to public and private signals and find that, on average, subjects put a larger weight on the public signal. However, the weight is smaller than in equilibrium and closer to level-2 reasoning. Stated second order beliefs indicate that subjects underestimate the information contained in public signals about other players’ beliefs, but this can account only for a part of the observed deviation of behavior from equilibrium. In the extreme case of a pure coordination game, subjects still use their private signals, preventing full coordination. Reconsidering the welfare effects of public and private information theoretically, we find for level-2 reasoning that increasing precision of public signals always raises expected welfare, while increasing precision of private signals may reduce expected welfare if coordination is socially desirable.coordination games, strategic uncertainty, private information, public information, higher-order beliefs, levels of reasoning

Three very simple games and what it takes to solve them

We study experimentally the nature of dominance violations in three minimalist dominance-solvable guessing games. Only about a third of our subjects report reasoning consistent with dominance; they all make dominant choices and almost all expect others to do so. Nearly two-thirds of subjects report reasoning inconsistent with dominance, yet a quarter of them actually make dominant choices and half of those expect others to do so. Reasoning errors are more likely for subjects with lower working memory, intrinsic motivation and premeditation attitude. Dominance-incompatible reasoning arises mainly from subjects misrepresenting the strategic nature (payoff structure) of the guessing games

Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches