Evolutionary stability of behavioural types in the continuous double auction

In this paper, we investigate the effectiveness of different types of bidding behaviour for trading agents in the Continuous Double Auction (CDA). Specifically, we consider behavioural types that are neutral (expected profit maximising), passive (targeting a higher profit than neutral) and aggressive (trading off profit for a better chance of transacting). For these types, we employ an evolutionary game-theoretic analysis to determine the population dynamics of agents that use them in different types of environments, including dynamic ones with market shocks. From this analysis, we find that given a symmetric demand and supply, agents are most likely to adopt neutral behaviour in static environments, while there tends to be more passive than neutral agents in dynamic ones. Furthermore, when we have asymmetric demand and supply, agents invariably adopt passive behaviour in both static and dynamic environments, though the gain in so doing is considerably smaller than in the symmetric case

Evolutionary Game Theory

Articl

Non-centralized Control for Flow-based Distribution Networks: A Game-theoretical Insight

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.Generalitat de Catalunya FI 2014Ministerio de Ciencia y Educación DPI2016-76493-C3-3-RMinisterio de Ciencia y Educación DPI2008-05818Proyecto europeo FP7-ICT DYMASO

Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified, and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics

Purely competitive evolutionary dynamics for games

We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.Comment: 13 pages, 6 figure

Stochastic evolutionary game dynamics

In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.Comment: To appear in "Reviews of Nonlinear Dynamics and Complexity" Vol. II, Wiley-VCH, 2009, edited by H.-G. Schuste