Table 1.
Comparison of characteristics of convergence application models by game theory.
Table 2.
Classic game framework of R&D investment strategy.
Fig 1.
Concept map for quantum information strategy game.
In the diagram, a ’Black Box’ represents the R&D system, and the cognitive attributes of the players are depicted as overlapping circles, labeled with ’Cognition’ and ’Mind’ for players named Alice and Bob, symbolizing their mental states and cognitive processes. The ’Observation’ section symbolizes the transition of these cognitive processes into actual behaviors or actions. The ’Potential State’ reflects the strategic options available to the players, corresponding to decisions like ’Cooperation’ and ’Defection.’ The probabilities of these strategies are represented in a manner akin to the squared magnitude of probability amplitudes in quantum mechanics, which calculates the likelihood of each strategy.
Fig 2.
Quantum information strategy game model.
Fig 2. illustrates the stages of a quantum information strategy game model: starting from a cooperative initial state, moving through an entanglement phase to introduce correlations, followed by strategy selection and development. It then progresses to disentangle and resolve the state, culminating in the measurement of outcomes to determine the players’ expected payoffs. Initial State: Both players start in a cooperative state |00⟩, represented on a Bloch sphere. Entangling Gate (U): An entangling operation introduces quantum correlations between the players. Initial Value Interpretation: The entangled state represents a mix of cooperative and competitive strategies. Strategy Selection (RA and RB): Players choose strategies affecting the game’s evolution. Entanglement Resolution (U†): The entangled state is resolved, setting the stage for payoff determination. Determination of Expected Payoff: The game concludes with a measurement that determines the players’ payoffs, represented by πA and πB.
Table 3.
Concept of quantum gate and strategy.
Fig 3.
Comparison of compensation systems according to combination of quantum strategies.
The image is a bar graph from a paper on quantum game theory. It depicts the expected payoffs for two players (Player A and Player B) across different combinations of quantum strategies. Each pair of bars represents a different strategic combination, with the height of the bar indicating the expected payoff. Player A’s payoffs are shown in blue, while Player B’s are in red. The graph is used to illustrate how different quantum strategies can affect the payoffs in a quantum game, demonstrating the dynamic interplay and the potential outcomes of strategic choices in this theoretical framework.
Table 4.
Payoff (πA, πB) according to combination of quantum strategies.
Fig 4.
Quantum circuit diagram when RA = X, RB = Y.
The image shows a quantum circuit for a two-qubit system, where specific operations are applied to simulate a game with strategies RA = X and RB = Y. The sequence includes rotations (Rz), controlled-NOT (CNOT) for entanglement, phase shifts (P), another set of rotations, and measurement operations, indicating the process of evolving the quantum state according to chosen strategies and then measuring the outcomes.
Fig 5.
Change in entanglement angle (γ) and expected payoffs of players A and B. The graph displays the relationship between the entanglement angle (gamma value) and the expected payoffs for players A and B. It depicts a bell-shaped curve, with the payoff values on the y-axis and the gamma values on the x-axis. The peak of the curve suggests the optimal entanglement angle where the expected payoffs for both players are maximized. This figure illustrates how varying degrees of entanglement affect the strategic outcomes in a quantum game when players adopt specific strategies, in this case, Pauli X for player A and Pauli Y for player B.
Table 5.
Comparison of R&D cartel, R&D bureaucracy, and R&D monopoly.