Evolution of Money Through Multi-Agent Model Abhishek Malik (Y6020) Abhishek Gupta (Y6019) Project Guide: Prof. Amitabha Mukerjee

Introduction Our objective: Proto-money from barter – Agent-Based Simulation for Emergence of Money from Barter Barter Issues Double Coincidence of Wants Storage of Wealth Conversion Rates Money Medium of Exchange Store of Value Unit of Account

Related Works: Kiyotaki and Wright Kiyotaki and Wright did game theoretic analysis of emergence of money through nash-equilibria search. (1989) “On Money as a Medium of Exchange” The Game Theoretic Approach

Money as a Medium of Exchange The Game Theoretic Approach It’s a simple general equilibrium matching model, in which the objects that become media of exchange will be determined endogenously as part of the non- cooperative equilibrium. The driving force behind the use of money is specialization, which implies that agents do not necessarily consume what they produce. (Adam Smith, 1776)

Money as a Medium of Exchange The Game Theoretic Approach We look for strategies that maximize individuals' expected utility, given the strategies of others and the distribution of inventories. Nash equilibrium in trading strategies is characterized. The Economy has three indivisible commodities 1, 2, and 3; equal proportions of three types of agents 1,2, and 3. Type I agents derive utility from the consumption of good i and only produce good i* /= i

Money as a Medium of Exchange The Game Theoretic Approach Expected Utility = (Utility derived from consuming i) – (disutility of producing i*) – (disutility of storing a good j) The agents trade among with some pre-defined constraints. Equilibrium is attained and there may be more than one commodities of exchange.

Related Works: Duffy Duffy and Ochs did a human subject based study based on Kiyotaki-Wright model in Duffy later performed agent-based model experiments with more encouraging results. (2001)

Related Works: Duffy In the 2001 Agent-based model study titled “Learning to speculate: Experiments with artificial and real agents” The two modifications to the Kiyotaki-Wright model were: 1.an unequal distribution of players across types 2.automating the decisions of all player types who are not called upon to play speculative strategies in equilibrium.

Related Works: Kobayashi et.al. M. Kobayashi et.al. use Doubly Structural Network Model (DSN model) (2009) DSN: – Inner-agent model of beliefs/knowledge – Inter-agent model of social-network It explain concept of money as exchangeable medium.

Related Works: Kobayashi et.al.

1.Exchange: neighboring agents i & j with probability P E if both recognize exchangeability between goods. 2.Learning: i.Imitation (P I ) ii.Trimming (P T ) iii.Conceiving (P C ) iv.Forgetting (P F )

Additions to Kobayashi Model Additions: 1.Production function a.P = f (health) 2.Consumption (demand distribution) 3.Health = f (consumption fulfillment) 4.Trade by utility from commodities a.Utility = (Demand/ Supply) b.Arranged in order for commodities and traded accordingly

References [1] Duffy, J., “Learning to speculate: Experiments with artificial and real agents”, Journal of Economic Dynamics & Control 25, pages (2001) [2] Kiyotaki, N., Wright, R., “On money as a medium of exchange”, Journal of Political Economy 97, pages (1989) [3] Kobayashi, M. et. al., “Simulation Modeling of Emergence-of-Money Phenomenon by Doubly Structural Network”, New Advances in Intelligent Decision Technologies, pages (2009)

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