# The Vote with the Wallet Game: Responsible Consumerism as a Multiplayer Prisoner's Dilemma
## 2 The Simplest Model Representation: A 2-Player Static Game  
In the simplest version of the game there are 2 players, \(i=1,2\), who can vote with the wallet for the SR product (\(vR\)) or for the standard product (\(vS\)). The payoff of player \(i\) is  
\[U_{i}(S)= \begin{cases}b+a-c&\text{if }S=(vR,vR)\\ \frac{1}{2}b+a-c&\text{if }S=(vR,vS)\\ \frac{1}{2}b&\text{if }S=(vS,vR)\\ 0&\text{if }S=(vS,vS)\end{cases}  \tag{1}\]  
where \(S:=(S^{i},S^{-i})\in\{vR,vS\}^{2}\) is the strategy profile. The payoff function (1) depends on three crucial factors: the public good benefit accruing from the choice of the SR product (\(b\in(0,+\infty)\)), weighted for the share of players choosing the strategy \(vR\), the enjoyment arising from players' other-regarding preferences (\(a\in[0,+\infty)\)), and the extra-cost of voting for the SR product (\(c\in[0,+\infty)\)). The first factor (\(b\)) is the economic benefit accruing to the individual from company behaviour change due to the vote with the wallet. This element hinges on the assumption that voters' actions have an impact on companies in proportion to the share of responsible voters and can direct them toward a more responsible behavior. Valuable examples of this benefit are higher chances of getting a job or higher job satisfaction in a more socially responsible company and health benefits or amenities in a more environmentally sustainable company. Other examples may relate to tax or cultural corporate responsibility. According to the former, consumers vote with the wallet for a company abstaining from tax dodging practices that reduce tax financed welfare services in their country. According to the latter, they vote with the wallet for a company that finances local cultural inheritance with its CSR policies. (An example of cultural corporate responsibility comes from Expedia, Inc., a world's leading online travel company establishing a partnership of the World Heritage Alliance with the UNESCO World Heritage Centre. The World Heritage Alliance includes 59 corporate members and partners (such as the Fairmont Hotels and Resorts and Mandarin Oriental) promoting environmental, cultural and social responsibility, and supporting local community tourism initiatives at World Heritage sites with grants or promotion in favour of responsible tourists contributions. The alliance is currently involved in the protection of 20 World Heritage sites in seven countries including Mexico, Costa Rica, Belize, Jordan, Dominica, Ecuador, and the United States. For other case studies of cultural corporate responsibility see [18; 19].) In all these cases it is reasonable to assume that the responsible vote with the wallet produces a utility for consumers through a benefit which has public good features since it is clearly non-rivalrous and non-excludable (a socially, environmentally, fiscally, or culturally responsible company cannot limit the enjoyment of its responsible stance to consumers voting for SR products excluding free riders voting for conventional products). (We consider \(b\) as exogenous for simplicity (and not related to oligopolistic models of CSR competition) since we focus on the perspective of consumers, who are reasonably assumed tohave their own approximate idea of the positive externality arising from the vote with the wallet and not to have a sophisticated knowledge of the competition model behind it.). The second factor (\(a\)) is the contribution, if any, of the responsible purchase to the utility function of the voter if she has some form of other-regarding preferences, an element which has been demonstrated not to be uncommon in the experimental literature. (Empirical findings from Dictator Games [20], Gift Exchange Games [21; 22]), Public Good Games [23; 24; 25], Trust Games [26; 27], Ultimatum Games [28; 29], provide ample evidence documenting the existence of other-regarding preferences.