This paper introduces discrete large games where the set of players is a countable dense ‘grid’ with a finitely additive distribution. In these games any function from player names to mixed actions is a legitimate strategy profile. No extraneous continuity or measurability conditions are assumed. Randomness can be modeled explicitly and an exact law of large numbers holds. Equilibria enjoy a st...

Let X(i), i t [0; 1] be a collection of identically distributed and pairwise uncorrelated random variables with common finite mean # and variance a 2. This paper shows the law of large numbers, i.e. the fact that ~ X ( i ) d i = #. It does so by interpreting the integral as a Pettis-integral. Studying Riemann sums, the paper first provides a simple proof involving no more than the calculation o...

We analyze the mathematical structure of models for large risk portfolios, especially for credit risk models. These risk portfolios are modelled using a multivariate mixture model for the dependence structure between the risks. The dependence structures are characterized by latent variables Θ, which play the role of the systematic risks. We show that, depending on the choice of the distribution...

This paper introduces a new model of environments with a large number of agents and stochastic characteristics. We consider sequences of finite but increasingly large economies that ‘discretize’ the continuum. In the limit we obtain a model that is continuum-like in important respects, yet it has a countable set of agents with a finitely additive, ‘uniform’ distribution. In this model, the law ...