2,184 research outputs found
Sion's mini-max theorem and Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group
We consider the relation between Sion's minimax theorem for a continuous
function and a Nash equilibrium in a multi-players game with two groups which
is zero-sum and symmetric in each group. We will show the following results.
1. The existence of Nash equilibrium which is symmetric in each group implies
Sion's minimax theorem with the coincidence of the maximin strategy and the
minimax strategy for players in each group. %given the values of the strategic
variables.
2. Sion's minimax theorem with the coincidence of the maximin strategy and
the minimax strategy for players in each group implies the existence of a Nash
equilibrium which is symmetric in each group.
Thus, they are equivalent. An example of such a game is a relative profit
maximization game in each group under oligopoly with two groups such that firms
in each group have the same cost functions and maximize their relative profits
in each group, and the demand functions are symmetric for the firms in each
group.Comment: 14 page
A Probabilistic Model for the Cold-Start Problem in Rating Prediction using Click Data
One of the most efficient methods in collaborative filtering is matrix
factorization, which finds the latent vector representations of users and items
based on the ratings of users to items. However, a matrix factorization based
algorithm suffers from the cold-start problem: it cannot find latent vectors
for items to which previous ratings are not available. This paper utilizes
click data, which can be collected in abundance, to address the cold-start
problem. We propose a probabilistic item embedding model that learns item
representations from click data, and a model named EMB-MF, that connects it
with a probabilistic matrix factorization for rating prediction. The
experiments on three real-world datasets demonstrate that the proposed model is
not only effective in recommending items with no previous ratings, but also
outperforms competing methods, especially when the data is very sparse.Comment: ICONIP 201
- …