We introduce a game of complete information with multiple principals and multiple common agents. Each agent makes a decision that can affect the payoffs of all principals. Each principal offers monetary transfers to each agent conditional on the action taken by the agent. We characterize pure-strategy equilibria and we provide conditions—in terms of game balancedness—for the existence of an equilibrium with an efficient outcome. Games played through agents display a type of strategic inefficiency that is absent when either there is a unique principal or there is a unique agent.
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