  The paper [Ras15a] introduced distribution-valued games. This game-theoretic
model uses probability distributions as payoffs for games in order to express
uncertainty about the payoffs. The player's preferences for different payoffs
are expressed by a stochastic order which we call the tail order.
  This thesis formalizes distribution-valued games with preferences expressed
by general stochastic orders, and specifically analyzes properties of the tail
order. It identifies sufficient conditions for tail-order preference to hold,
but also finds that some claims in [Ras15a] about the tail order are incorrect,
for which counter-examples are constructed. In particular, it is demonstrated
that a proof for the totality of the order on a certain set of distributions
contains an error; the thesis proceeds to show that the ordering is not total
on the slightly less restricted set of distributions with non-negative bounded
support. It is also shown that not all tail-ordered games have mixed-strategy
Nash equilibria, and in fact almost all tail-ordered games with
finitely-supported payoff distributions can only have a Nash equilibrium if
they have a pure-strategy Nash equilibrium.
  The thesis subsequently extends an idea from [AM19] and proposes a new
solution concept for distribution-valued games. This concept is based on
constructing multi-objective real-valued games from distribution-valued games
by segmenting their payoff distributions.
