You are cordially invited to the SCL seminar of the Center for the Study of Complex Systems, which will be held on Thursday, 29 November 2018 at 14:00 in the library reading room “Dr. Dragan Popović” of the Institute of Physics Belgrade. The talk entitled
Evolutionary Dynamics Approach to Biological All-Pay Auctions
will be given by Dr. Aleksandra Alorić (Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade).
Abstract of the talk:
This talk will offer a brief introduction to game theory and a physicist’s approach to game-theoretical questions. Especially, we will address games where the space of available actions is not discrete but continuous, e.g., instead of deciding whether to cooperate or defect like in Prisoner’s dilemma, an agent decides how long (s)he will stay in a conflict, like in War of Attrition game.
Competition for resources in biological context bears a resemblance to auction mechanisms, many agents compete but only a few (or only one) get the reward. Contrary to the well-studied auction models in economics, a reasonable assumption in this context is that everybody (not only the winner) pays their bid, e.g. time/energy invested to endure a conflict or foraging food. In this talk, we will describe the dynamics of the k-player all pay auctions searching for the states that evolution might favour. We will analyze these systems with an associated birth-death process governed by the success of an agent’s strategy in the repeated interactions modeled as k-player all-pay auctions. In the large population limit, where the stochasticity can be neglected, we will derive replicator equations whose fixed points are previously found Evolutionary Stable Strategies for these games. However, in previous works cycles were also noted that could not be explained at the level of deterministic description. We will thus introduce back the stochasticity (the diffusion approximation) and the intrinsic noise which, as we will show, gives rise to the cyclic dynamics. We observe that the cycles are more present when the bidding strategy space is smaller, and when the number of participants in an auction (k) is small.
 K. Chatterjee, J. G. Reiter, and M. A. Nowak, Evolutionary dynamics of biological auctions, Theor. Popul. Biol. 81, 69 (2012).
 J. G. Reiter, A. Kanodia, R. Gupta, M. A. Nowak, and K. Chatterjee, Biological auctions with multiple rewards, Proc. R. Soc. B 282, 20151041 (2015)
 A. Alorić, T. Galla, and P. Sollich, Noise-induced cycles in biological all-pay auctions, Manuscript in preparation (2018).