Risk aversion in economic transactions

Most people are risk-averse (risk-seeking) when they expect to gain ( lose). Based on a generalization of expected utility theory which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long-term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once forever for each operator) and the rules ( e. g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.