1. Alternating-offers Bargaining problems A Co-evolutionary Approach Nanlin Jin, Professor Edward Tsang, Professor Abhinay Muthoo, Tim Gosling, Dr Maria Fasli, Dr Sheri Markose, Guannan Wang http://cswww.essex.ac.uk/Research/CSP/bargain Funding This research has been partly funded by BT and University of Essex Contact For more information, visit: Computational Finance: http://cswww.essex.ac.uk/Research/CSP/finance Center for Computation Finance and Economic Agents: (CCFEA) http://www.cfea-labs.net For possible collaboration, contact: Professor Edward Tsang Phone: +44 1206 872774; email: edward@essex.ac.uk Nanlin Jin Phone: +44 1206 872771; email: njin@essex.ac.uk Evolutionary Computation Evolution Computation, inspired by nature, has been proved successful in studying adaptive systems. It is especially good for non-linear, epistatic, large search- space problems. Basic Alternating-Offers Bargaining Problem Bargaining theory studies a class of bargaining situations where two players have common interests, usually called “cake”, but conflict over how the cake is divided. Under the “No delay” and “Stationarity” assumptions, Perfect Equilibrium Partition (P.E.P) of the basic Alternating-Offer Bargaining is: Technical Overview More Realistic Assumptions Co-evolutionary System For the bargaining problem, co-evolution is required as (a) the fitness is assessed by bargaining outcomes between strategies from co-evolving populations; and (b) the two players may have different information. Observations Cake Partitions by Co-Evolution: In general, co-evolutionary system can find out approximate solutions with low cost and reasonable time. Experimental agreements distribute within the P.E.P neighbourhood. Observations Co-adaptive Learning: Strategies modify in beneficial ways to adapt to dynamic environments through reinforcement ‘learning’. Usually both players’ behaviours and bargaining outcomes stabilize near to P.E.P after a sufficiently long leaning period. Run time:100 runs last for only about 1 or 2 days Conclusions  Strategies do ‘learn’ to perform better during co- evolution process.  And, experienced players make more efficient agreements with less money left on table.  Excluding situations with extreme discount factors, co- evolution processes converged to bargaining agreements that cluster around P.E.P, even under much weak assumptions.  Co-evolution can be regarded as an effective complementary and approximate method to the economics theoretical approach.  This framework is ready for us to study more complex bargaining problems with few modifications. People Computer Scientists Economists Evolution Process:  A set of candidate solutions is called a “population”;  Survival of fittest: the better performance, the higher possibility to be selected as parents of the next generation;  Crossover and Mutation: modifications used to generate the next generation. In Biology, co-evolution is defined as reciprocal evolutionary change in interacting species. Department of Computer Science Department of Computer Science Sheri Markose Director CCFEA Abhinay Muthoo Expert in Bargaining Theory Edward Tsang Computational Finance & Economics Maria Fasli TAC Auction Riccardo Poli Genetic Programming Nanlin Jin Evolutionary Bargaining Theory Guannan Wang Bargaining Software Tim Gosling Distributed Constraint satisfaction A Generation 2 B -Generation 2 A Generation 1 A Generation 0 A Generation nB -Generation n B -Generation 1 B -Generation 0 i.Players are allowed to take any division of the cake, if share x i  (0, 1]; ii.Players have neither the knowledge of P.E.P nor the intelligent reasoning ability as economists. But players have the basic common senses, that are: the higher payoff the better, and the higher bargaining cost the lower payoff. iii.One player doesn’t know the other’s behaviours before bargaining starts; => bounded rationality In situations when we are unable to compute the P.E.P., can we evolve sensible bargaining strategies? Where X * A and X * B are the optimal share for A and B, respectively,  A and  B are their discount factors