Game Development Reference
In-Depth Information
In Apt et al. [2008] only strict preferences were considered and so defined
finite games with parametrised preferences were compared with the concept
of CP-nets (Conditional Preference nets), a formalism used for representing
conditional and qualitative preferences, see, e.g., Boutilier et al. [2004].
Next, in Roux et al. [2008] conversion/preference games are intro-
duced. Such a game for n players consists of a set S of situations and for
each player i a preference relation
i on S and a conversion relation
i on S . The definition is very general and no conditions are placed on the
preference and conversion relations. These games are used to formalise gene
regulation networks and some aspects of security.
Finally, let us mention another generalisation of strategic games, called
graphical games , introduced by Kearns et al. [2001]. These games stress
the locality in taking a decision. In a graphical game the payoff of each player
depends only on the strategies of its neighbours in a given in advance graph
structure over the set of players. Formally, such a game for n players with the
corresponding strategy sets S 1 ,...,S n is defined by assuming a neighbour
function N that given a player i yields its set of neighbours N ( i ). The payoff
for player i is then a function p i from × j∈N ( i ) ∪{i} S j to R.
In all mentioned variants it is straightforward to define the notion of a
Nash equilibrium. For example, in the conversion/preferences games it is
defined as a situation s such that for all players i ,if s → i s , then s i s .
However, other introduced notions can be defined only for some variants.
In particular, Pareto e ciency cannot be defined for strategic games with
parametrised preferences since it requires a comparison of two arbitrary
joint strategies. In turn, the notions of dominance cannot be defined for the
conversion/preferences games, since they require the concept of a strategy
for a player.
Various results concerning finite strategic games, for instance the IESDS
Theorem 1.3, carry over directly to the strategic games as defined in Osborne
and Rubinstein [1994] or in Apt et al. [2008]. On the other hand, in the
variants of strategic games that rely on the notion of a preference we cannot
consider mixed strategies, since the outcomes of playing different strategies
by a player cannot be aggregated.
1.7 Mechanism design
Mechanism design is one of the important areas of economics. The 2007 Nobel
Prize in Economics went to three economists who laid its foundations. To
quote from The Economist [2007], mechanism design deals with the problem
Search Nedrilad ::

Custom Search