Research in Economics
Working papers and publications | Economic Miscellany
Applied Game Theory
Coauthor: Alexei Parakhonyak.
We consider a dynamic (differential) game with three players competing against each other. Each period each player can allocate his resources so as to direct his competition towards particular rivals - we call such competition targeted. We show that if the players are myopic, the weaker players eventually lose the game to their strongest rival. If instead the players are sufficiently non-myopic, then each player concentrates more on fighting his strongest opponent. Consequently, the weaker players grow stronger, the strongest player grows weaker and eventually all the players converge and stay in the game. Targeted competition setting can be applied to a wide variety of cases: competition between firms, competition between political parties, warfare.
Coauthor: Maarten Janssen.
We consider an oligopolistic market where firms compete in price and quality and where consumers are heterogeneous in knowledge: some consumers know both the prices and quality of the products offered, some know only the prices and some know neither. We show that two types of signalling equilibria are possible. Both are characterised by a dispersion and Pareto-inefficiency of the price/quality offers. But, better price/quality combinations are signalled with lower prices in one type and with higher prices in the other type. For common consumers’ preferences it is the first type: the cheapest offer – the best deal.
If a consumer faces two products of the same kind but different in their prices and quality, which one does he choose? I show that if firms compete in both prices and quality, and if there are some consumers on the market who do not search for the best offer, then the competition is always such that it is best for a consumer to buy the cheapest product. In an equilibrium the quality will either grow with price but not sufficiently, or it will fall with price. The result holds for a wide class of consumers' preferences.
Risk and Rationality
Taking the current wealth as a reference point and differentiating between gains and losses helps in explaining the choices people make (Markowitz, Kahneman and Tversky). However, this approach violates asset integration and does not explain why people tend to differentiate between gains and losses in the first place. The classical expected utility approach is theoretically more sound but fails descriptively. In this work I analyse a setting when there are extra transaction costs associated with losses. I show that expected utility with such transaction costs is equivalent to differentiation between gains and losses around a reference point without such transaction costs. Hence, depending upon whether transaction costs are accounted for or not, one or the other approach will seem suitable to explain individual choice.
Mathematical Finance
In this paper I address the problem of pricing options in the presence of transaction costs. A known approach to this problem is a so-called superhedging approach. I suggest an idea of hedging sets and, based on it, a new algorithm to implement the superhedging approach. As far as I know, only European options were discussed in the literature on pricing derivatives when there are transaction costs. The proposed algorithm, however, can be applied to price American options as well. It is also more efficient compared with the previous methods. Examples of using the new algorithm to price European and American options when there are transaction costs are provided.
Research in Economics