Why is the market rallying?

When a market is not doing well, investors are suffering from devaluation of their assets, they have to two choices: hold or sell (we do not consider the case of buying more, as we assume their priority is to stop further losses and both are risk averse). They could hold their assets in the hope of asset prices will recover in the future. Or they can sell their assets to avoid further losses. To simplify the problem, I assume there are only two investors making decisions at the moment.

	hold	sell
hold	-b+a,-b+a	-(b+c),-b
sell	-b,-(b+c)	-b-d,-b-d

At the beginning, both investors have losses of -b. If both investors hold, then their losses will maintain or even be cut, as when no trading happens, the price will maintain at its original level; moreover, if there is a new investor entering the market, this could increase the price . If one decides to hold, the other decides to sell, then the one who chooses to hold will have a greater loss as selling could decrease the price, and the other who chooses to sell will prevent from future losses and limit his/her losses. Both traders decide to sell, both will suffer greater losses (d>c). Such game does not play for once, this is a repeated-game. In real life, different investors have different costs of their assets and their expectation of their assets' future values; therefore, they will not continue with one choice, though both choosing to hold is the best strategy can provide the best outcomes in the repeated games. In general, when the market is rallying together to push up prices, it signals most investors are suffering losses from the devaluation of their assets.