Monopoly Deal: A Benchmark Environment for Bounded One-Sided Response Games

Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. Typically, these games fall into three categories based on the flow of control: strictly-sequential (where players alternate single actions), deterministic-response (where some actions trigger a fixed outcome), and unbounded reciprocal-response (where alternating counterplays are permitted). A less-explored but strategically rich structure exists: the bounded one-sided response. This dynamic occurs when a player's action briefly transfers control to the opponent, who must satisfy a fixed condition through one or more sequential moves before the turn resolves. We term games featuring this mechanism Bounded One-Sided Response Games (BORGs).