Perturbed best response dynamics in a hawk-dove gameforthcoming in Economics Letters
with Volker Benndorf READ ABSTRACT
We study a model that linearly interpolates between the evolutionary one- and two-population structures in a hawk-dove game and examine the impact of behavioral noise on equilibrium selection. Perturbed best response dynamics generates two hypotheses in addition to the bifurcation predicted by standard replicator dynamics. First, when replicator dynamics suggests mixing behavior (close to the one-population model), there will be a bias against hawkish play. Second, polarizing behavior as predicted by replicator dynamics in the vicinity of the two-population model will be less extreme in the presence of behavioral noise. We find both effects in our data set. |
A quantum-like model for complementarity of preferences and beliefs in dilemma games
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We propose a formal model to explain the mutual influence between observed behavior and subjects’ elicited beliefs in an experimental sequential prisoner’s dilemma. Three channels of interaction can be identified in the data set and we argue that two of these effects have a non-classical nature as shown, for example, by a violation of the sure thing principle. Our model explains the three effects by assuming preferences and beliefs in the game to be complementary. We employ non-orthogonal subspaces of beliefs in line with the literature on positive-operator valued measure. Statistical fit of the model reveals successful predictions. |
Equilibrium selection with coupled populations in hawk-dove games:
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published in the Journal of Economic Theory 165 (2016) 472-486
with Volker Benndorf and Hans-Theo Normann |
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Standard one- and two-population models for evolutionary games are the limit cases of a uniparametric family combining intra- and intergroup interactions. Our setup interpolates between both extremes with a coupling parameter κ. For the example of the hawk–dove game, we analyze the replicator dynamics of the coupled model. We confirm the existence of a bifurcation in the dynamics of the system and identify three regions for equilibrium selection, one of which does not appear in common one- and two-population models. We also design a continuous-time experiment, exploring the dynamics and the equilibrium selection. The data largely confirm the theory.
Quantum stochastic walks on networks for decision-making
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Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making. |
Do preferences and beliefs in dilemma games exhibit complementarity?
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Blanco et al. (2014) show in a novel experiment the presence of intrinsic interactions between the preferences and the beliefs of participants in social dilemma games. They discuss the identification of three effects, and we claim that two of them are inherently of non-classical nature. Here, we discuss qualitatively how a model based on complementarity between preferences and beliefs in a Hilbert space can give an structural explanation to two of the three effects the authors observe, and the third one can be incorporated into the model as a classical correlation between the observations in two subspaces. Quantitative formalization of the model and proper fit to the experimental observation will be done in the near future, as we have been given recent access to the original dataset. |
Games with type indeterminate players
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We develop a basic framework encoding preference relations on the set of possible strategies in a quantum-like fashion. The Type Indeterminacy model introduces quantum-like uncertainty affecting preferences. The players are viewed as systems subject to measurements. The decision nodes are, possibly non-commuting, operators that measure preferences modulo strategic reasoning. We define a Hilbert space of types and focus on pure strategy TI games of maximal information. Preferences evolve in a non-deterministic manner with actions along the play: they are endogenous to the interaction. We propose the Type Indeterminate Nash Equilibrium as a solution concept relying on best-replies at the level of eigentypes. |
A connection between quantum decision theory and quantum games:
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published in the Journal of Mathematical Psychology 58 (2014) 33-44
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Experimental economics and studies in psychology show incompatibilities between human behavior and the perfect rationality assumption which do not fit in classical decision theory, but a more general representation in terms of Hilbert spaces can account for them. This paper integrates previous theoretical works in quantum game theory, Yukalov and Sornette’s quantum decision theory and Pothos and Busemeyer’s quantum cognition model by postulating the Hamiltonian of Strategic Interaction which introduces entanglement in the strategic state of the decision-maker. The Hamiltonian is inherited from the algebraic structure of angular momentum in quantum mechanics and the only required parameter, θ ∈ [0,π], represents the strength of the interaction. We consider it as a non-revealed type of the decision-maker. Considering θ to be a continuous random variable, phenomena like learning when participating in repeated games and the influence of the amount of disposable information could be considered as an evolution in the mode and shape of the distribution function. This modeling is motivated by the Eisert–Wilkens–Lewenstein quantization scheme for Prisoner’s Dilemma game and then it is applied in the Ultimatum game, which is not a simultaneous but a sequential game. Even when this non-revealed type θ cannot be directly observed, we can compute observable outcomes: the probabilities of offering different amounts of coins and the probability of the different offers being accepted or not by the other player.
Directed random markets: Connectivity determines money
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Boltzmann–Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this paper, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear. |
