1. **State the problem:** We have a 3x3 game matrix with strategies Cassava, Rice, Soy for player Zhansaya and Banana, Mango, Pineapple for player Anish. The payoffs are given as pairs $(Zhansaya, Anish)$ for each strategy combination. 2. **Matrix of payoffs:** $$\begin{array}{c|ccc} & \text{Banana} & \text{Mango} & \text{Pineapple} \\ \hline \text{Cassava} & (4,0) & (0,4) & (7,3) \\ \text{Rice} & (6,3) & (7,0) & (4,2) \\ \text{Soy} & (5,7) & (8,8) & (1,9) \end{array}$$ 3. **Definition of Nash equilibrium:** A strategy profile where no player can improve their payoff by unilaterally changing their strategy. 4. **Find best responses:** - For each of Anish's strategies, find Zhansaya's best response (highest first payoff). - For each of Zhansaya's strategies, find Anish's best response (highest second payoff). 5. **Zhansaya's best responses:** - Against Banana: payoffs are 4 (Cassava), 6 (Rice), 5 (Soy). Best is Rice. - Against Mango: payoffs are 0 (Cassava), 7 (Rice), 8 (Soy). Best is Soy. - Against Pineapple: payoffs are 7 (Cassava), 4 (Rice), 1 (Soy). Best is Cassava. 6. **Anish's best responses:** - Against Cassava: payoffs are 0 (Banana), 4 (Mango), 3 (Pineapple). Best is Mango. - Against Rice: payoffs are 3 (Banana), 0 (Mango), 2 (Pineapple). Best is Banana. - Against Soy: payoffs are 7 (Banana), 8 (Mango), 9 (Pineapple). Best is Pineapple. 7. **Check for Nash equilibria:** A Nash equilibrium is a cell where both players are playing best responses. - (Cassava, Banana): Zhansaya's best response to Banana is Rice, so no. - (Cassava, Mango): Anish's best response to Cassava is Mango, Zhansaya's best response to Mango is Soy, so no. - (Cassava, Pineapple): Anish's best response to Cassava is Mango, so no. - (Rice, Banana): Zhansaya's best response to Banana is Rice, Anish's best response to Rice is Banana, so yes. - (Rice, Mango): Anish's best response to Rice is Banana, so no. - (Rice, Pineapple): Anish's best response to Rice is Banana, so no. - (Soy, Banana): Anish's best response to Soy is Pineapple, so no. - (Soy, Mango): Anish's best response to Soy is Pineapple, so no. - (Soy, Pineapple): Anish's best response to Soy is Pineapple, Zhansaya's best response to Pineapple is Cassava, so no. 8. **Conclusion:** The only Nash equilibrium is at (Rice, Banana) with payoffs (6,3). **Final answer:** There is exactly 1 Nash equilibrium in this game.