Game Theory at HHL

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The awarding of the Nobel Prize in Economic Sciences 2014 to the French Economist Jean Tirole has once again emphasized the importance of game theory in economics and social sciences. Tirole has made outstanding contributions to the investigation of markets and their regulation. In his research, he applied methods of game theory, which he further developed en passant.

“Game theory“ or “interactive decision theory” analyses situations in which several persons have to make decisions, and where the individual well-being depends on the choices of all persons. Hence, any person also has to take into account the possible decisions of the others.

Most situations in life actually are interactive decision situations, i.e., games. Hence, game theory is a versatile tool for the social sciences. Now, what does it mean to do research in this field, i.e., to develop the tool box that game theory provides? To answer this question, we should look back in history.

Game theory was born during World War II and the early fifties of the last century. Some of the smartest people at Princeton, mostly mathematicians, were assigned to better understand the interaction with the enemy and to make recommendations to politicians and the military. They started to study simple games with clear rules. Because of their education, they took a mathematical perspective.

By studying mathematically described games, one tries to model the important aspects of reality and to neglect “unimportant” issues. Applying mathematical methods moreover leads to a purifying abstraction, a very stringent argumentation and – last but not least – a stronger interest of mathematical talents in social sciences. Therefore, those who do research in game theory need a profound understanding of mathematics.

At HHL, game theoretic research is conducted at the group of “Economics and Regulation“. Where recently, André Casajus (below, left) and Frank Hüttner (below, right), who is funded by the German Research Foundation (DFG), were particularly successful with their research and published an article in the prestigious Journal of Economic Theory.

Dr Andre Casajus_links_ Dr Frank Huettner_rechts_HHL

Mainly, their work is concerned with the fair distribution of jointly generated gains of cooperation. In order to get an idea about their result, consider the following example. Three cities have decided not to build three separate waste water treatment plants but to use one such plant together. This way, overall costs are lower, i.e., their cooperation is profitable. How should the benefits of the joint plant be distributed among the three communities?

The literature provides a default answer to this question. It is obtained by using a formula that has been introduced and motivated by Lloyd S. Shapley (awarded with the Nobel Prize in 2012) already in 1953. His suggestion rests on the participants’ own contributions to the gains of cooperation. In this sense, his solution is performance-based.

Casajus and Hüttner (2014, below) wonder how the gains of cooperation could/should be distributed in a more solidary fashion. The answer they give seems to be simple: any participant first obtains the performance-based payoff as suggested by Shapley. Then, the payoff is taxed at a certain rate (the higher the tax the more solidary). Finally, the overall tax revenue is distributed equally.

The justification for this rule being a good one rests on a complicated mathematical argument that also covers more general situations. Details and further references can be found in the article below.

Casajus, A., & Huettner, F. (2014),  Weakly monotonic solutions for cooperative games, in: Journal of Economic Theory 154, 162-172