Prof. Krzysztof Apt

Abstract:

In this lecture we survey our recent research on social network games. They are tailored to study a model of social networks introduced by Apt and Markakis in 2011 in which the nodes influenced by their neighbours can adopt one out of several products. In these games the payoff of each player weakly increases when more players choose his strategy, which is exactly opposite to the congestion games.

In particular we show that these games may have no Nash equilibrium and that determining an existence of a Nash equilibrium is NP-complete. We also clarify the status and the complexity of the finite best response property (FBRP), the finite improvement property (FIP).

Further, we exhibit in this framework some paradoxes. One of them allows us to explain `bubbles' in a financial market, in which a decision of a trader to switch to some new financial product triggers a sequence of transactions, as a result of which all traders involved become worse off.

(Joint work with Evangelos Markakis and Sunil Simon)