Entrega

F ig u r e 5.1: Searching th rou gh “static" and “stra teg ic” lan d scap es. T h e to p diagram is a represen­ ta tio n o f a G A ’s search on a on e-d im en sio n a l la n d sca p e.T h e x -a x is rep resen ts th e choice variable; th e fu nction to be m axim ised is “h ard” in th at it has d isco n tin u ities and m u ltip le local m a x im a — it is taken from an ex a m p le given by H olland (1992). T h e “s ta tic ” gen etic algorith m efficiently sam p les p oin ts from th e set o f p o ssib le choices. In th e “stra teg ic” problem , th ere are tw o in d ep en d en t choice variables, and each is rep resen ted on an axis. T h e tw o zig-zagged lines should be read as rep resen ting p ay-off m a x im a for one agent keeping fixed th e behaviou r o f th e oth er agent. For a given agent 1 str a te g y choice (x-aixis p o sitio n ), agent 2 ’s gen etic algorith m searches for a good solu tion (p oin t on th e solid line); th e good so lu tio n s are represented on th e diagram as th e lines o f “b est resp on ses” to every agent 1 choice. And for every choice by the agent 2 G A , agent I ’s g en etic algorith m searches for a “go o d resp o n se” . Pure stra teg y N ash equilibria occur w hen each player is bid ding a b est respon se to th e oth er— th a t is, where th e b est-resp o n se fu n ction s cross. C o -evolu tion arises from th e rep etition and in teraction o f th ese step s. T h e relation betw een co -ev o lu tio n , C ournot d y n a m ics and fictitio u s play d y n a m ics o f te x tb o o k econ om ics (for ex a m p le (B in m ore 1992, C hapter 9 )) is very close: in th e C ournot d y n a m ic, you pick a str a te g y to sta rt, th en p lay b est respon ses un til you reach a restin g p oin t (if ever)— th ese are show n as “N E ” p oin ts in th e exam p le; in th e co -evolu tion ary d y n a m ic, you pick a p oin t and play resp on ses in (ap p ro x im a tely ) proportion to th eir past success.

C H APTER 5. THE PROMISE OF AGENT-BASED MODELS 163

always seem in danger of disappearing into a recursion because for agent A to do best, it must know what agent B will do. Simultaneously, agent B needs to know what agent A will do before deciding what to do. Fictitious play is just one way of thinking our way out of such a recursion; it is a sort of step by step approach th at says - “Let the first agent optimise behaviour keeping the other agents’ behaviour as if th at were a fixed element of the environment; let all agents do this in tu rn '\

Fictitious play dynamics have been investigated by game theorists (see Fu- denberg and Levine (1998) for an overview), especially for cases where the strategy spaces are small and easily knowable (and where there is only learn­ ing about others’ behaviour). Fudenberg and Levine mention the genetic algorithm ( Fudenberg and Levine (1998, Section 4.9)) as a candidate learner in cases where the strategy space is l a r g e . I n Curzon Price (1997) and Cur­ zon Price (1999), each agent is represented as a genetic algorithm; the genetic algorithm codes for strategies; a “market simulation” represents the fixed parts of the world ( “physics” , engineering parameters . . . ) and the rules determining the outcome of tournaments; these tournaments are played be­ tween strategies picked from different firms; the outcomes in the market simulation determine strategy payoffs; every so often, these payoffs are used to “update” each agent’s strategies using the genetic algorithm dynamics

(crossover and mutation, with associated parameters)

Fudenberg and Levine (1998) offer criticism of the use of “social learning” GAs in strategic modeling.

These models are m odels of private as opposed to social learning. Whereas the dis­ tinction is now well understood (see Vriend (1998) for a discussion), it was not always so at the tim e of Curzon Price (1997). For example, Marks and Schnabl (1999) contains a public learning G A contrasted to a private learning neural net. The authors do not differentiate effects due to the algorithm and those due to the learning environment; they

C H APTER 5. THE PROMISE OF AGENT-BASED MODELS 164

This structure is intended to be a reduced form for some of the strategic learning th at occurs within firms: the firm is like a GA; within the firm, many strategies are “up for consideration” .^^ The firm regularly generates new strategic possibilities; the board or the pricing committee selects strategies in proportion to their past scores (or by chance, if they have never been used). A selected strategy is then tested in the market. This means th at it needs to do well relative to the strategies employed within other firms, and not within its own firm. Each firm is thought of as conducting this process, so co-evolution is about the strategies of one firm affecting the payoffs to the strategies of the other firm.

The correspondence between learning in the firm and learning in a GA population is clearly very rough. Maybe the most troubling approximation is th a t firms typically do not have actual performance data on most of the strategies that they select for trial. Instead, they rely on counterfactual rea­ soning, inference, theory, gut instinct, consultants’ reports, bankers’ advice and much more ... If a firm is strategically astute, it will even have its own model of how other firms have modeled i t . .. A challenging extension of the simple GA models used here would be the inclusion of a model of the evolu- attribute all differences to the learning algorithm.

^^Why not model these interior processes explicitly, rather than rely on the crude re­ duced form offered by the GA? Ideally, we would want to model within the firm, and within each agent, and even within each conflicting “will” of each agent . . . Stopping the m odeling at some point is an entirely pragmatic decision— project tim etable, feasibility, com puting resources.

^^The fact that a firm may have models of how other players have modeled its represen­ tation of the strategic environment is a version of the familiar game theoretic recursion of “my best choice depends on your best choice, depends on my best choice . . . ” An indica­ tion of the practical significance to management of strategic effects relating to perceptions of the firm’s model of the environment is the effort that many companies devote to offering industry and market trend analysis for public consumption. In these exercises, firms are saying “this is how we see the environment” .

C H APTER 5. THE PROMISE OF AGENT-BASED MODELS 165

tion of firms’ perceptions of their environment to be used to assess candidate strategies.