Rock-Paper-Scissors with No Rock

This question is about an asymmetric zero-sum game where one player has a restricted action set. It takes the familiar rock-paper-scissors framework and removes one option for your opponent, forcing you to rethink what "balanced play" means when the usual symmetry of the game is broken. On MyQuantPartner, it sits in the game theory and strategic reasoning section of our quant prep content.

It trains your intuition for mixed-strategy equilibria when players have different feasible moves, and for interpreting payoff matrices under constraints. You practice reasoning about optimal randomization, indifference conditions, and how expected value changes when one side is handicapped.

This matters in quant interviews because market-making, optimal execution, and trading against constrained counterparties all resemble such games. Interviewers use it to test applied game theory, comfort with expected value, and clean probabilistic thinking under strategic interaction.

What it tests

Whenever a game restricts the set of available actions for one or both players, the structure of optimal mixed strategies shifts: the Nash equilibrium is found by making each opponent's remaining choices equally unattractive, so they cannot exploit any bias in your play. The key is to set your own probabilities so that, given the opponent's constraints, they are indifferent between their available options, and vice versa. This is achieved by equating expected payoffs across the opponent's choices, which leads to a system of equations whose solution gives the equilibrium strategies. The principle holds because, in zero-sum games, any deviation from this balance can be exploited by the other player, so equilibrium is reached only when neither can improve by unilaterally changing their strategy. This logic generalizes to any finite game where the action set is asymmetric or restricted, not just classic rock-paper-scissors.