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Alternating-offers Bargaining problems A Co-evolutionary Approach

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Alternating-offers Bargaining problems A Co-evolutionary Approach. A Generation 0. B -Generation 0. A Generation 1. B -Generation 1. A Generation 2. B -Generation 2. A Generation n. B -Generation n. Edward Tsang Computational Finance & Economics. Maria Fasli TAC Auction.

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Alternating-offers Bargaining problems

A Co-evolutionary Approach

A Generation0

B -Generation 0

A Generation 1

B -Generation 1

A Generation2

B -Generation 2

A Generationn

B -Generationn

Edward Tsang


Finance & Economics

Maria Fasli

TAC Auction

Riccardo Poli



Guannan Wang



Nanlin Jin


Bargaining Theory

Tim Gosling


Constraint satisfaction

Abhinay Muthoo

Expert in

Bargaining Theory

Sheri Markose



Department of

Computer Science

Nanlin Jin, Professor Edward Tsang, Professor Abhinay Muthoo, Tim Gosling, Dr Maria Fasli, Dr Sheri Markose, Guannan Wang


Computer Scientists


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.


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.
  • Players are allowed to take any division of the cake, if share xi(0, 1];
  • 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.
  • One player doesn’t know the other’s behaviours before bargaining starts;
  • => bounded rationality

In Biology,co-evolution is defined as reciprocal evolutionary change in interacting species.

Where X*A and X*B are the optimal share for A and B, respectively, A and B are their discount factors

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.


For more information, visit:

Computational Finance:

Center for Computation Finance and Economic Agents: (CCFEA)

For possible collaboration, contact:

Professor Edward Tsang

Phone: +44 1206 872774; email: [email protected] Jin

Phone: +44 1206 872771; email: [email protected]

  • 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.


This research has been partly funded by BT and University of Essex

In situations when we are unable to compute the P.E.P., can we evolve sensible bargaining strategies?