In this work, we aim to answer the question-what triggers cooperative behaviour in the thermodynamic limit by taking recourse to the Public goods game. Using the idea of mapping the 1D Ising model Hamiltonian with nearest neighbor coupling to payoffs in game theory we calculate the Magnetisation of the game in the thermodynamic limit. We see a phase transition in the thermodynamic limit of the two player Public goods game. We observe that punishment acts as an external field for the two player Public goods game triggering cooperation or provide strategy, while cost can be a trigger for suppressing cooperation or free riding. Finally, reward also acts as a trigger for providing while the role of inverse temperature (fluctuations in choices) is to introduce randomness in strategic choices.

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Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting feature in this scenario, when the quantum discord of Alice's qubits increases, then the quantum discord of Bob's prepared qubits decreases. Furthermore, we show that the fidelity of one-qubit quantum teleportation using Bob's prepared qubits as the channel is higher than using Alice's qubits.

The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and quantum game of Chicken. A phase transition is seen in both games as function of the entanglement in the game. We observe that for maximal entanglement irrespective of the classical payoffs, majority of players choose quantum strategy over defect in the thermodynamic limit.Quantum game theory is an important extension of classical game theory to the quantum regime. The classical games might be quantized by superposing initial states, entanglement between players or superposition of strategies, for a brief account see [1]. The outcomes of a quantum game is well known for two player case however, we want to investigate the scenario when the number of players goes to infinity, i.e., the thermodynamic limit. In recent times, there have been attempts to extend the two player classical games to the thermodynamic limit by connecting it to the Ising model [2,3,4]. We do a similar analysis and connect two player quantum games to the 1D Ising model in the thermodynamic limit to figure out the strategy chosen by majority of Shubhayan Sarkar