In this course on game theory, we will be studying a range of mathematical
models of con°ict and cooperation between two or more agents. The course
will attempt an overview of a broad range of models that are studied in
game theory, and that have found application in, for example, economics
and evolutionary biology. In this Introduction, we outline the content of
this course, often giving examples.
In a symmetric Nash Equilibrium the prices of both goods are randomized in an
atomless fashion for the most part of the parameter space apart from the case when the
two goods are strongly substitutable in which case the less valuable good is not sold at
all. Only when the goods are either independently valued or are substitutes is it feasible
that the two prices are randomized independently. When the goods are complements
and one of the goods is priced high the other can not be priced in the upper part of
its support implying local negative correlation between the two prices.
In social networks, since nodes generally belong to di®erent authorities and
pursue di®erent goals, they will not cooperate with others unless cooperation can
improve their own performance. Thus, how to stimulate cooperation among nodes in
social networks is very important. However, most of existing game-theoretic cooper-
ation stimulation approaches rely on the assumption that the interactions between
any pair of players are long-lasting.
While peer-to-peer (P2P) video streaming systems have achieved promising
results, they introduce a large number of unnecessary traverse links, which con-
sequently leads to substantial network ine±ciency. To address this problem and
achieve better streaming performance, we propose to enable cooperation among
group peers, which are geographically neighboring peers with large intra-group up-
load and download bandwidths.
In this chapter we discuss the types of imperfect competition and examine a particular type called oligopoly. Our goal in this chapter is to see how this interdependence shapes the firms’ behavior and what problems it raises for public policy.