I need help with generating three things: payoff matrices of an asset market, price vector of the securities market, and arbitrage portfolios. A typical question is structured as follows:

Suppose there are two states of nature in the future. In the asset market, there are the two contingent claims, one for each state. There's a third security with payoffs x=(4,1). Suppose the prices of the contingent claims are both 1/2: p(c(s₁))= p(c(s₂))=1/2. The price of the third security is 3.

I'm not interested in just specific answers to this question. Frameworks for further use are what I'm after. Thanks.