نمای کلی از برنامه های اخیر نظریه بازی برای بیوانفورماتیک

The goal of this work is to provide a comprehensive review of different Game Theory applications that have been recently used to predict the behavior of non-rational agents in interaction situations arising from computational biology. In the first part of the paper, we focus on evolutionary games and their application to modelling the evolution of virulence. Here, the notion of Evolutionary Stable Strategy (ESS) plays an important role in modelling mutation mechanisms, whereas selection mechanisms are explained by means of the concept of replicator dynamics. In the second part, we describe a couple of applications concerning cooperative games in coalitional form, namely microarray games and Multi-perturbation Shapley value Analysis (MSA), for the analysis of genetic data. In both of the approaches, the Shapley value is used to assess the power of genes in complex regulatory pathways.

Game Theory is a mathematical theory dealing with models for studying interaction among decision makers (which are called players). Since the seminal book by John von Neumann and Oskar Morgenstern (1944) ‘Theory of Games and Economic Behavior’, it is usual to divide Game Theory into two main groups of interaction situations (which are called games), non-cooperative and cooperative games. Non-cooperative games deal with conflict situations where players cannot make binding agreements. In cooperative games all kinds of agreement among the players are possible. In non-cooperative games each player will choose to act in his own interest, keeping into account that the outcome of a game depends on the actions of all the players involved. Actions by players can be simultaneous (the ‘stone, paper, scissors’ game or the ‘matching pennies’ game) or at several points in time (chess, backgammon). Cooperative games deal with situations where groups of players (which are called coalitions) coordinate their actions with the objective to end up with joint profits which often exceed the sum of individual “profits”.1 The terms bioinformatics and computational biology are often used interchangeably [17]. However, bioinformatics more properly refers to the creation and advancement of theory and of algorithms to solve formal and practical problems arising from the management and the analysis of biological data. In order to extract useful information from data produced by high-throughput biological techniques such as genome sequencing, bioinformatics uses mathematical tools. A representative problem in bioinformatics is the study of gene regulation to perform expression profiling using data from microarrays or other technologies (see for instance, [8], [16] and [42]). Other common problems are the analysis of mutations in cancer, the evolution of virulence and the HIV infection, etc. In this paper, we review some applications of Game Theory to the analysis of biological data. Obviously, such applications are not aimed at answering normative issues, like giving an advice to a group of variables (e.g. genes) on how they should behave inside a biological cell. In this context, Game Theory is used to describe the behavior of variables and to predict the outcome of their interaction [35]. Of course, a critical issue of all these applications of Game Theory to experimental data is a meaningful definition of the notion of “profit”. The possibility of extending the concept of profits, benefits, savings or whatever could be in the interest of each decision maker to be maximized on her/his own count, is a well-known feature of Game Theory applications. In Game Theory, the term “profit” usually is more correctly replaced by utility value of a rational player. We do not want to enter here the discussion of how an utility function is defined and why it is a numerical representation of the preferences of a rational decision maker. For introductions to this problem see for instance the books by Kreps [21]. In Section 2, we introduce evolutionary games and their application in modelling the evolution of virulence. Section 3 deals with coalitional games and their applications to gene expression data analysis. Section 4 concludes.

In this paper, some recent applications of evolutionary Game Theory and coalitional games to computational biology and bioinformatics were discussed. Although such applications fall in different categories of game theoretical models, respectively, non-cooperative and cooperative games, it is evident that all of them succeeded in applying the classical paradigm of rationality to describe the interaction of agents (e.g. genes) which do not fit with the classical assumption of rational agents. Then, we argue that the next generation of studies in the field will be aimed at providing a different interpretation of rationality axioms in the context of biological data analysis. We conclude with the remark that, since computational biology deals with the basic “ingredients” of evolution, it should be very interesting to attempt to combine evolutionary Game Theory and coalitional games to explain why and which cooperative strategies are more successful if they are subject to evolutionary pressure.