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Modeling reciprocity in games

Final Report Summary - RECIPROCITY (Modeling reciprocity in games)

Reciprocal behavior is crucial in socio-economic interactions from the friendly exchange of gifts to international relationships between countries. An agent, be it a person, firm, or country, is said to be reciprocal if it responds in a friendly manner to a friendly action of another agent or retaliates in response to a hostile action. Examples of this behavior are everywhere: people return favors done by their friends; in many traditional societies reciprocity is commonly used to facilitate economic transactions and cooperation in the absence of law enforcement; governments tend to unnecessarily match the trade restrictions introduced by other countries even at a cost to themselves.

The main objective of the project was to build a tractable model of reciprocity in strategic environments (games) which incorporates knowledge from variety of social sciences including economics, anthropology, and evolutionary psychology. In particular, the goal was to find mathematical framework that would allow to analyze situations in which agents have preferences over beliefs of others and where agents are capable to reason about intentions of others.

The second goal of the project was to experimentally test the hypotheses of the model. In particular, the experiments were planned which would allow to estimate the relative strength of people's preferences over the beliefs of others about them and to test how well the model fits the data.

Many a study has shown that interactions between economic agents are influenced by considerations regarding the beliefs of others and others' intentions (for example describing incentives and punishments in a job contract). However, there are hardly any tractable models of reciprocity that would allow applied economists to study these phenomena. Current project was intended to provide the tools for applied economists and policy makers to analyze strategic situations in which agents are reciprocal or have some other forms of preferences over beliefs of other agents. In addition, in experimental part of the project the methodology was developed that can help future researchers to test hypotheses regarding the preferences over beliefs and intentions.

The main results include the following. The model achieves the desired objectives: it captures the notion of preferences over beliefs; allows agents to reason about the intentions of others as the game unfolds; and makes it easy to predict the behavior in variety of games. This is in contrast to the existing models in the literature where ad hoc assumptions regarding the behavior of the agents are made and the analysis of even simple games is rather complicated. Experiments conducted so far demonstrate that people have strong tendency to act upon their hypotheses about the beliefs of other players. The model fits well to the observed data.

Game theory has shown its usefulness in many areas of applied social sciences from anthropology to political science. Current research provides new tools that can be used by social scientists and policy makers alike to make better predictions and/or devise better policies. For example, the model developed in this project can help to better understand the optimal design of contracts; interactions among political parties; sustainability of voluntary cooperation; and the interworking of developing economies where economic transactions are still facilitated by traditional societal relationships rather than free market.