  In this expository paper we illustrate the generality of game theoretic
probability protocols of Shafer and Vovk (2001) in finite-horizon discrete
games. By restricting ourselves to finite-horizon discrete games, we can
explicitly describe how discrete distributions with finite support and the
discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are
naturally derived from game-theoretic probability protocols. Corresponding to
any discrete distribution with finite support, we construct a finite-horizon
discrete game, a replicating strategy of Skeptic, and a neutral forecasting
strategy of Forecaster, such that the discrete distribution is derived from the
game. Construction of a replicating strategy is the same as in the standard
arbitrage arguments of pricing European options in the binomial tree models.
However the game theoretic framework is advantageous because no a priori
probabilistic assumption is needed.
