International trade and strategic behaviour: a game theoretical analysis of the trade dispute between Turkey and Russia

Abstract Starting from the premise that strategic interactions between countries influence trade policy decisions, this paper is a first attempt at exploring the possible outcomes of a trade dispute between Turkey and Russia, assuming that Turkey can lodge a complaint about Russia’s protectionist move to the WTO Dispute Settlement Body (DSB). Employing the course of events during the recent economic conflict between the two countries, the article models the stages of a trade game wherein players exhibit non-cooperative behaviour. It finds that Turkey reporting Russia to the DSB depends on the cost of the dispute, which represents both economic losses and losses that can be considered disadvantages in a broader sense. The results show that in trade relations where asymmetric interdependence is observed, if both parties mutually commit to an international organisation, binding regulations may provide strategy options that are otherwise infeasible for the disadvantaged player.


Introduction
Political economy explanations of trade policies help us to understand the structure of trade protection as well as the process of related policy formation. Nevertheless, it is not possible most of the time to choose permanent policies towards trade, since interests of countries may change as production structures and development levels change. As a result, several forms of strategic interaction appear during the trade policy-making process, which require close scrutiny.
The extant literature on related research mostly consists of attempts to model trade relations in a game-theoretical framework, emphasising how trade policy strategies can be interpreted to the strategies of a game. Indeed, trade policy decisions fit well to the strategic nature of decisions in game theory, where each player anticipates the choices of the other player(s), before deciding which course of action to take over a number of possible actions. KEYWORDS turkey; Russia; trade dispute; trade policy; World trade organization (Schewe, 2013(Schewe, , p. 1178. In this sense, Russia's membership to the WTO in 2012 was hoped to 'increase the transparency and predictability' of the country's trade policy moves (Schewe, 2013(Schewe, , p. 1171. We therefore introduce WTO Dispute Settlement Body to our model in order to diversify possible strategies and related outcomes.
The game starts with a trade sanction initiated by Russia against Turkish imports, leading to a dispute with Turkey. 1 Turkey in return notifies the DSB about Russia's protectionist move, and the game evolves. In the model, we take inspiration from the commonly used basic game-theoretical structure and avoid more complex models. However, we depart from the existing research by identifying a trade conflict between two real economies asymmetric in size and strategic in bilateral trade, in a model which includes the reputational gains and losses of being involved in a dispute. We also introduce time-dependent variables in the game and assume that the payoffs differ. We further perform a repeated game in order to seek whether repetition of the same game might foster cooperation.
The study is structured as follows. The second section introduces the model and its variables. The third section defines the stages followed by the designation of a setting where possible payoffs from a trade dispute are arranged. An extensive non-cooperative trade game between Turkey and Russia including the influence of the WTO is also presented in this section. The fourth section describes dominant strategies and Nash equilibria, followed by the repeated game. The fifth section offers concluding thoughts.

The model and the variables
In the analysis, the players, strategies and possible outcomes of a trade game are presented to define a trade dispute between Turkey and Russia. In the game, Turkey can notify to the DSB of Russia's trade protectionist move.
Assume that Turkey is the complainant (T C ) in a trade dispute with Russia, where the latter is the respondent (R R ). That is, Russia has taken an action of trade restriction and is accused by Turkey of having violated the WTO law. The players, strategies and outcomes of the game can be seen in Figure 1. The nodes of the extensive form game are constituted according to the stages of the WTO Dispute Settlement Mechanism (DSM). Stages of the dispute where bilateral negotiations are likely to occur are also shown in Figure 1.
In the game, Turkey's (Player 1) payoff is given before Russia's (Player 2) payoff in parentheses and payoff components belonging to either Turkey or Russia are denoted by subscripts T and R respectively. The variables are defined as follows: f T and f R : Gains from bilateral trade for Turkey and Russia respectively before Russia's trade restrictions. The values of f T and f R may not be equal to each other since the economic gains derived from bilateral trade may be different for the two countries due to the composition and volume of trade.
t: Time period as a particular section of the dispute settlement process. t 1 is the time period between trade restriction and notification, t 2 is the period between notification and panel, t 3 is the period between panel and appeal, t 4 is the period between appeal and implementation appeal. c t : Cost of Russia's protectionist move for Turkey, including both the economic losses and losses that can be considered as disadvantages in a broader sense. c t is also the amount that Turkey demands from Russia as compensation and its value is assumed to be proportional to the time the trade restriction is in action, t. g t : Value that Russia gains due to its trade protectionist move, including both the economic gains and the gains that can be considered as advantages in a broader sense. This may not be the same as c t , since such a protectionist move may bring additional gains to Russia due to its advantaged position 2 in this particular trade dispute. The value of g t is also assumed to be proportional to the time the trade restriction is in action, t. n: Amount that is subject to negotiation during the consultations which Russia would aim to subtract from the amount Turkey demands as compensation, 0 ≤ n ≤ ct . Though it is not possible to name the exact amount of n, it can be expected that Russia is going to have the bargaining power due to its high elasticity of demand 3 for Turkish imports. Thus, for Russia, n is going to equal to 0 at worst and c t at best. d: Legal and organisational cost of undergoing the dispute settlement system, or the economic value of the dispute costs for each party in each turn of the dispute settlement process. For simplicity, we assume that the value of d is equal for both parties. 4 . If Turkey chooses to proceed in the game, the dispute costs will start to accumulate periodically (i.e. d, 2d, 3d, 4d). r acc , r l , r g : When a notification is made to the WTO, it is publicly known. r acc is the reputation loss for Russia of being accused in public. r l is the reputation loss to either Russia or  Turkey in case of a negative outcome of the dispute settlement process. r g is the reputation gain for either party in case of a positive outcome of the process.
x: Number of turns in the dispute process, [1 ≤ x ≤ 4]. With all alternating strategies and related outcomes in place, we construct four turns in the game, to be in line with the first four stages of a typical dispute settlement process within the WTO. 5 p: Probability that Turkey's notification is a case violating the WTO rules, due to the type of case which -according to its magnitude, its match with various goals and priorities of the related government and its economic or political impact -determines the 'damage' it generates. 1−p on the other hand, is that the case is considered as discrepant by the WTO authorities.
The game is designed under the complete information assumption. Under this assumption, both players are equally informed about their own case and the past WTO dispute cases. Thus, differences in the players' expectations, if there are any, are negligible. The game is not played under perfect information, since in that case there would have been knowledge of actions inside the game.
It can be difficult to estimate exactly how a certain trade policy measure affects another country. Although trade conflicts have occurred between Turkey and Russia before, it would be hard to estimate the exact cost of a prospective dispute due to the dynamic nature of the trade volume and investment level between the two countries. However, as members of the WTO, both Turkey and Russia would have pre-information, based on earlier trade disputes among members, on the possible number of turns (x) before a dispute is solved, as well as on the probability that a case presented to the WTO would either be accepted p or rejected 1−p .

Stages of the game
The theoretical framework presented in the analysis aims for the WTO to be involved in the setting as a mediator that the players of the game apply, in order to look for possible solutions to the trade dispute. Assuming that Turkey cannot implement retaliation measures independent from the WTO, if Turkey chooses to notify, then acceptance of the complaint by the organisation gives the country the opportunity to recover its costs.
Here, it should be noted that there is nothing Turkey can do to determine or to influence the form of the trade sanctions imposed by Russia. The sanctions are in their final form, designed by the owner country. Thus, as can be seen in the reduced game in Figure 2, all utilities after the panel is established, except for the dispute cost, are dependent on whether the case is accepted as a trade violation or not by the WTO authorities.
This requires Turkey to have a good observance and understanding of WTO rules and dispute settlement procedures in order to correctly estimate the evolution of the game. The unknown dispute cost is represented by xd.
When a player in a node is linked with another one with broken lines in the figure, it means that the player cannot determine which of these two nodes it is at when it must choose, but all possible payoffs are still known to both players, in line with the complete information assumption.
Going back to the extensive form game in Figure 1, evaluating the nodes of the game can provide policy suggestions and predictive outcomes. At the fourth node, there are two possible outcomes: either Russia is the loser of the panel report or Turkey is. Consider first that the panel approves the case and that Russia is the loser of the report. If Russia chooses not to appeal, the panel report should be adopted within the period t 3 . In that case, utility to be derived is going to be: If, on the other hand, Russia appeals but the case is approved, it has to adopt the report within the period t 4 which leads to the expected payoff: If Turkey is the loser of the panel report and chooses not to appeal, Russia will not have to step back from its trade sanctions. Thus, the loss for Turkey is going to be: If, on the other hand, Turkey appeals, but the case is rejected by the Appellate Body, the country has to adopt the Appellate Body's decision within a short period of time, t 4 . In that case, Turkey is going to be facing the utility: Out of 501 disputes which have been brought to the WTO between 1995 and 2015, the complainant or the respondent party has chosen to appeal only in 65 disputes following the  panel report. Among the 65 disputes, none of the Appellate Body reports has found that the Panel has completely erred in its legal findings. 6 Indeed, most reports are not completely approving or dismissive but instead they approve some parts of the complaint and dismiss other. This indicates that the panel reports contain accurate decisions in a majority of the cases. Thus, Russia must either strongly believe the probability of its appeal being accepted is higher in this particular case or the amount of compensation Turkey demands (c t ) must be very large in order to take the risk of appealing. According to a local news agency, the economic cost of the trade dispute between Russia and Turkey in 2008 was around $1 billion at the time it was settled. 7 Although the dispute lasted three months, the cost for the Turkish side accounted for almost one-fifth of the value of total exports from Turkey to Russia in 2007, which was $4.7 billion. According to an assessment by the EBRD economists, Russia's sanctions against Turkey in November 2015 are expected to 'reduce Turkey's GDP growth in 2016 by around 0.3-0.7 percent, if they persist over the year and are fully applied' . The same assessment shows, on the other hand, that 'the impact on Russia's GDP will be limited, with some moderate pressure on import prices and inflation' . 8 According to an economist's statement to the BBC, 'the cost for Turkey in lost business could be at least $10 billion' , while the country 'risks losing $3.5 billion annually in income from Russian tourists, and another $4.5 billion annually through the cancellation of construction projects' . 9 A report issued by one of Turkey's biggest banks, Is Bankasi, on the impact of Russian sanctions, supports this estimate, with a 'worst-case scenario amount of $7.3 billion' . 10 Turkish Deputy Prime Minister also declares a close estimate of $9 billion, adding that 'the tension is likely shave 0.3 to 0.4 percent off Turkey's GDP ' . 11 In a dispute case, Turkey can demand dispute costs close to those put forward in these estimates as compensation from Russia, which in turn may cause Russia to take the risk to appeal. Besides, amounts as such may prompt Turkey to choose to notify the WTO about Russia in the first place when the trade dispute in question occurs.
Depending on Russia's decision, Turkey could then either comply, or accept a defeat, or start retaliating. The latter two possibilities can affect future bilateral economic relations. Reflections of the retaliation possibility, for instance, can be seen on prospective investment projects as well as future trade contracts. If, on the other hand, the complaint is dismissed by the panel, Turkey can choose between: and At the third node, Turkey is to choose either to demand the establishment of a panel or not. If it chooses not to demand the establishment of a panel, related utility function is going to be: while the choice to establish a panel may result in either: uT C (panel|approve) = p ct 3 − 2d + r g or: depending on whether the case is approved or rejected by the panel, respectively. Thus, the complete utility function for Turkey for demanding a panel is:

Turkey chooses to demand a panel if:
Here it should be noted that not to demand a panel is not a rational strategy for Turkey once the country complains to the WTO. Since all utility functions are known in advance, Turkey would not choose not to demand a panel strategy if it knew that would be its best expected outcome when it could choose to do nothing in the first place and get 0 in return.
The second node represents the consultation process of the WTO's dispute settlement, where in our setting Turkey and Russia try to reach a settlement on their own, based on negotiations. However, since all players' utilities are supposed to be known from the beginning in bargaining processes, each player knows which outcome one prefers over another. In this case, there is no need for bargaining at all since it is possible to trace the optimal mutually acceptable solution at once. Hence, if there is an agreement acceptable to everybody, we may say directly what the agreement will be, and this agreement will be offered by the first player in the first round of the negotiation. The intuition behind this reasoning is based on the Rubinstein Bargaining Model (Morrow, 1994). In our game, the choice to offer the agreement or not belongs to Russia, as it is to choose whether to give Turkey an acceptable offer or not. This is consistent with the intuition that Russia in such a situation in reality would consider doing the same, due to its significant economic ties with Turkey. It should be noted here that although Turkey is in a relatively disadvantaged position in its trade with Russia, Russia too has gains from this relationship not to be easily forsaken. On the other hand, since it is Russia who is assumed to have initiated the trade violation, and is the advantaged party, one may expect it to have the bargaining power in this process.
At this node, the value of n will be subject to negotiation. Turkey would prefer n to be equal to zero and Russia would prefer n to be equal to c t . If we assume that Russia makes the offer, it will start by offering Turkey nothing (n = ct). However, an offer at this stage with ct 2 − n − d should be greater than the payoff led by the 'not settle' strategy −ct 2 − d , otherwise it is unacceptable for Turkey. This means that Turkey will only accept offers where n < 2 − ct 2 .
When choosing whether to offer an acceptable size of n to Turkey or not, Russia's decision will depend on whether it prefers the payoff that the settlement strategy will produce or the one it will get when Turkey demands the establishment of a panel. The latter will result in either: Adding these together, the complete utility function for Russia if it chooses not to settle is: Russia's utility function for settling with Turkey is:

The decision equation for Russia at this point is to settle if
At the beginning, Russia chooses between free trade and initiating a trade restriction. Given that Russia draws a protectionist measure in its trade with Turkey, at the first node Turkey should decide whether to convey the case to the WTO level, by notifying the DSB. Turkey is assumed to have zero while Russia is assumed to have gt − f R , as the respective payoffs, when Turkey chooses the strategy 'do nothing' . Here, Turkey should compare two utility functions, given that it notifies, that Russia chooses to settle and that Russia chooses not to settle and consequently Turkey goes for a panel. That is, uT C (settle) = ct 2 − n − d and uT C panel = p r g − r l − 4d − ct 3 − 2d respectively. Turkey chooses to notify if it knows that the relevant function is greater than zero (which will be the outcome if it does not notify at all); otherwise it would not notify. As of January 2016, more than 80% of the complaints brought to the WTO have been approved. Thus, the high probability that the case would be approved would be crucial for the players, confirming the implications of the analysis.

Dominant strategies and Nash equilibria
In order to find out the dominant strategies, the game can also be shown in strategic form as in Table 1. Out of six strategies (and four relevant payoffs) shown in the table, it is then possible to track those that could be Nash equilibria. Table 1. strategic form game.
Out of six possible strategies in the game, the third and the fourth strategies seem to be Nash equilibria, which are N − P, S and N − P, NS respectively. These results show that once Russia imposes the sanctions against Turkey, Turkey as a rational player with complete information will always choose to notify and to panel, no matter if the countries settle or not in the end. Therefore the strategic form game can be reduced to the following form shown in Table 2.

Repeated game
In real economic relations, players usually do not interact once and for all as in single shot games. In cases where a dispute has occurred, recurrence of the game is even more meaningful to alter the non-cooperative outcome. Therefore, a repeated game is performed in this section to portray whether cooperation might be fostered. Klimenko, Ramey, and Watson (2008) have shown that external enforcement might serve achieving cooperation in recurrent trade agreements, particularly when mechanisms such as delays in dispute settlement and direct penalties are activated. We take inspiration from this idea and the model's basic assumptions. The authors build their model on the choice of tariff levels within trade agreements; instead, we adapt the idea to our stage game where the game starts with a dispute between Turkey and Russia. Turkey complains about Russia to the DSB and the countries negotiate on a compensation set to reach agreed-upon tariffs to proceed with pre-dispute bilateral trade. Complete information assumption holds in the repeated game and the DSB still exists as the institution to which players can apply in cases as needed. The DSB is further assumed to be keeping the history of the previous trade violations, complaints, negotiations and settlements. In the stage game, it was found that Turkey would always choose to notify and further panel once Russia implemented trade sanctions. This finding is embraced in the repeated game. By doing so, it is guaranteed that the presence of the DSB, when actively utilised, makes a difference in terms of the outcome.
Following Klimenko et al. (2008), it is assumed that the dispute solution within the DSB's dispute settlement process takes place with delay. Since policies chosen by the countries during the dispute resolution process do not matter for the DSB in terms of settlement, the players are likely to choose Nash equilibrium strategies. However, the countries are aware of the cost that the delay in dispute settlement entails, which in turn might foster cooperation.
The punishment mechanism for the defecting player in the repeated game works in two ways. First, after defection, the payoff for the defecting player is lower than the cooperative strategy payoff but the joint value of the relationship is still valid. In this setting, bargaining power is not fixed and assumed to be dependent on the history. In other words, if one player defects from cooperation it is going to have a reduced bargaining power and less of the joint value in future negotiations (Klimenko et al., 2008, p. 4).

Settle (S)
Not settle (NS) Notify, panel (N-P) (ct 2 − n − d, gt 2 − ct 2 + n − d − r acc ) (pc − xd, gt 2 − pc − xd − r acc ) Consistent with the 2015 dispute between Turkey and Russia, we assume that the period starts with a 'dispute state' as denoted by the DSB. This is where the dispute settlement process begins, and if settlement is achieved, DSB switches the state immediately from 'dispute' to 'cooperation' with probability p. Note that this probability is exogenous, and cannot be raised or lowered by the players, implying that dispute settlement process cannot be influenced by the disputing members. Countries continue negotiating henceforth, under the assumption that their negotiation strategies depend on history. Immediate switching vice versa, from 'cooperation' to 'dispute state' as soon as a trade violation occurs, is in line with our finding in the stage game that Turkey always chooses to notify the WTO's DSB about Russia.
When the DSB switches the state from 'dispute' to 'cooperation' , countries choose from a set of payoffs U C and report it to the DSB. If the dispute cannot be resolved, with the probability of 1 -p, the state remains as 'dispute' in the next period, independent of the actions chosen by the players in the current period. This time, countries choose from a set of U D , which in principle can be identical to U C .
For given sets of U C and U D , expected continuation payoffs can be as follows, implying that if the dispute is solved, u 1 , u 2 is chosen from U C in the following period, and if it is not solved, (u where: for s = C:(û 1 , û 2 ) ∊ U C , and u 1 1 , u 1 2 , u 2 1 , u 2 2 ∊ U E ; and s = D: (û 1 , û 2 ), u 1 1 , u 1 2 , u 2 1 , u 2 2 ∊ U E . When the game is in the dispute state, all continuation payoffs are chosen from U E . Once the 'cooperation state' is achieved, deviation from agreed tariffs ̂1 and ̂2 leads to the 'dispute state' , where continuation payoffs are again from U E .
We denote the set of payoff profiles that are supportable in state s by S S (U C , U D ). U C and U D are state-dependent sets of recurrent agreements under the following conditions: s = C, D, for each u 1 , u 2 ∊ U S u 1 , u 2 maximises the sum of the countries' payoffs on the set S S and (U C , U D ). This assumption requires that each player does its best in each state.
There exists (u � 1 , u � 2 ) such that each player gets an equal share of the joint value which is defined relative to a disagreement point consistent with agreement in the following period (for i = 1, 2), where: for s = C: (u � 1 , u � 2 ) ∊ U C and for s = D:(u � 1 , u � 2 ) ∊ U E Continuation payoffs are always chosen from U C or U D , but the countries cannot change the state as part of their agreement.
Within this framework, Klimenko et al. (2008) provides evidence that dispute costs, in particular the high ones, foster cooperation. This finding seems reasonable for our setting in that both reputation and dispute settlement costs cannot be negligible for trading partners such as Turkey and Russia.

Conclusion
Over the last two decades, Turkey and Russia have become major trading partners and energy cooperation is the most significant component of this trade relation. Nevertheless, economic relations between the two countries depicts a lopsided characteristic in favour of Russia due to Turkey's dependence on Russian gas. To rate the extent to which Russia may use this advantage as an actor in trade disputes, we present a game-theoretical model with all possible moves and outcomes of a WTO dispute settlement process between the two countries. With all the basic assumptions in place and the expected best moves for each player revealed, we find that the variables c t and p are essential in our setting. That is, we find under a complete information assumption that Turkey chooses to convey the case to the DSB if the value of the dispute cost in question is not negligible and that with higher probability it expects -based on information about earlier cases -that its complaint will be approved.
The flow of the game shows that if the players cannot settle and the case reaches a panel, the players' payoffs in the following nodes vary according to the panel's legal findings and to whether Russia complies or not. If Russia does not comply, Turkey may either choose to retaliate or it lodges an implementation appeal. It may also choose to do nothing. If Turkey chooses the implementation appeal strategy, it will have to face higher dispute costs and there is no guarantee whether its appeal will be approved. On the other hand, if Turkey chooses to retaliate, the countermeasure(s) should be constituted to cover the size equal to its economic loss caused by Russia's protectionist move. In such a case, Turkey should have previously made progress at least in finding markets alternative to Russia, with comparable transportation costs for its exports, in addition to its import demand elasticity for natural gas imports. Otherwise, the retaliation option would not be beneficial.
Another finding of our analysis is that in the consultation process, the choice to offer a mutually acceptable offer for agreement belongs to Russia as the first player in the first round. We also show in our model that not to demand a panel is not a rational strategy for Turkey once the country notifies to the WTO.
Finally, repeating the stage game may contribute to achieving cooperation in that both reputation and dispute settlement costs for the two countries are not negligible.
Recent trade conflicts between the two countries make the research up-to-date, relevant and of current importance for international economic relations. Continuation of the analysis provided in this study might encourage and shape the further development of the relationship between Turkey and Russia to a new level even more cooperative in all spheres, thus making relations healthier.

Notes
1. This assumption starting the game is strongly in line with real life. Russia imposed a series of economic sanctions against Turkey after Turkey downed a Russian warplane in November 2015. These sanctions included a ban on Turkish imports of certain agricultural produce and food, prohibition of hiring new Turkish workers and restriction of future Turkish economic activities, a 75% reduction in the number of international road transport permits for Turkish companies, reinforcing safety controls in Russian waters and seaports; abeyance of bilateral economic cooperation programmes and commissions, a ban on bilateral charter flights, a recommendation by the state tourism agency to suspend sales of Turkey holidays to Russian