先讲义双边IPR均衡。可以采用NE逻辑：如果w国提供IPR保护，a国也实行IPR保护（即互惠的IPR国民待遇）的条件是：企业从两国市场得到的利润可以弥补研发成本（满足企业的参预约束）；从政府效用函数出发，IPR保护要占优于公共研发形式。但此时存在协调问题，当研发成本可以在一国得到回收时，只需要一国实行严格的产权保护即可，很可能是在较大的市场实行严格的IPR保护，但两国均有激励进行弱的IPR保护，最终谁获得这种地位取决于历史因素，而这种格局一旦形成，便具有路径依赖。

NE逻辑的另一部分，假定w不提供IPR保护，a国了不提供IPR保护的条件是：单方面的IPR保护是非有效的，或者单边面的IPR保护被公共提供占优。
   可以对该NE解进行系统的博弈论求解。可以得到两国的支付矩阵：

可以看出，以上均衡取决于几个关键的参数x，k，d， 。相关的观察可以得到评论1.
Remark 1(The Symmetric Case: Inefficiencies).Suppose the two countries, a and w, have identical markets and are equally innovative. Then there are parameters d,, k and subject matter x for which, in equilibrium, (a) unilateral protection is efficient but R&D is publicly sponsored;(b) bilateral protection is efficient but R&D is publicly sponsored;(c) public sponsorship is efficient but both countries provide intellectual property protection; and (d) R&D investments are not made because neither country protects the subject matter or provides public sponsorship.

评论1给出了对称情形下非效率的几种情形，而引入IPR统一的依据在于这它可以对部分低效均衡进行修正。IPR统一有两种极端的形式，在两国遇到IPR纠纷时，或采取零保护（least protective harmonization），或采取完全保护（most protective harmonization）。可以得到评论2.
Remark 2(The Symmetric Case: Harmonization).Suppose the two countries, a and w, have identical markets and are equally innovative. Each of the following holds for some parameters d,,k and subject matter x:(a)in both the least protective and most protective harmonizations,R&D is publicly sponsored even though unilateral protection in one of the countries would be efficient;(b)in the most protective harmonization,countries harmonize on subject matters for which unilateral protection would be efficient; and(c)in the least and most protective harmonizations,the countries harmonize on subject matters for which public sponsorship is efficient but would not be provided.

在这里，我们并没有看清楚，IPR统一化对福利的影响。可能需要进入其具体的推导过程中才能捕捉到细微的差别。

非对称的市场规模
可以对基准模型进行扩展。如引入市场的不对称及研发能力的不对称。假定国家w具有更大的市场，但两国的研发能力相同。支付矩阵如下：

        相关的结论由评论3给出：
Remark 3(Asymmetric Markets: Inefficiencies).When the sizes of the regional markets are different, but the countries have the same innovative capacities, then each of the following holds for some parameter values, k and subject matter x:(a)unilateral protection is efficient but R&D is publicly sponsored;(b)unilateral protection in the smaller country is efficient, but the larger country provides it;(c)bilateral protection is efficient, but R&D is publicly sponsored;(d)public sponsorship is efficient, but both countries protect the subject matter; and(e)R&D investments are not made because neither country protects the subject matter or provides public sponsorship.

从以上结论可以看出，3b提供了新的元素，且可以发现，统一的IPR可以有助于解决问题3e。（公共研发的特征是什么？在一国福利框架下）
     评论4总结了统一的IPR政策对均衡结论的修正：
Remark 4(Asymmetric Markets: Harmonization).Suppose that the sizes of the regional markets are different, but the countries have the same innovative capacities. Then the country with the smaller market prefers more extensive harmonized protections than the country with the larger market.Further,each of the following holds for some parameters d,,k and subject matter x:(a)in both the least protective and most protective harmonizations,R&D is publicly sponsored even though unilateral protection in one of the countries would be efficient;(b)in the most protective harmonization,countries harmonize on subject matters for which unilateral protection would be efficient;(c)in the least protective harmonization,R&D is publicly sponsored even though harmonized protection would be efficient;(d)in the most protective harmonization,bilateral protection is provided even though public sponsorship is efficient and would otherwise be provided; and(e)in the least and most protective harmonizations,bilateral protection is provided even though public sponsorship is efficient, because public sponsorship would not alternatively be
Provided.

以上结论表明，在具有相同的研发水平下，市场规模较小的国家具有更强烈的IPR统一化动机，这可以解释瑞士、芬兰等国家对IPR的强烈渴求，但不能解释另外一些国家，如美国，具有较大的市场，同时也具有强烈的IPR需求，因而，作者想引入其它IPR决定因子，如研发能力。

异质的研发能力
现在看异质的研发能力。令 为a国与w国的研发产品数量，并假定 。可以得到与上一部分相平行的评论。
Remark 5(Asymmetric Innovative Capacities: Inefficiencies).Suppose the two countries a and w have identical markets but one is more innovative than the other. Then there are parameters d,, k and subject matter x for which, in equilibrium, (a) unilateral protection is efficient, but R&D is publicly sponsored;(b) bilateral protection is efficient, but R&D is publicly sponsored;(c) public sponsorship is efficient, but both countries provide IP protection; and (d) R&D investments are not made because neither country protects the subject matter or provides public sponsorship.
     引入统一的IPR后，可以得到评论6：
Remark 6(Asymmetric Markets: Harmonization).Suppose that the sizes of the regional markets are the same, but the countries have different innovative capacities. Then the country with more innovative capacity prefers more extensive harmonized protections than the country with less capacity.Further,each of the following holds for some parameters d,,k and subject matter x:(a)in both the least protective and most protective harmonizations,R&D is publicly sponsored even though unilateral protection in one of the countries would be efficient;(b)in the most protective harmonization,countries harmonize on subject matters for which unilateral protection would be efficient;(c)in the least and most protective harmonizations,both countries will protect subject matters for which public sponsorship is efficient but would not be provided;(d)in the least protective harmonization,R&D is publicly sponsored even though harmonized protection would be efficient; and(e)in the most protective harmonization,bilateral protection is provided even though public sponsorship is efficient and would otherwise be provided.

该评论得到的新的结论是，研发能力较强的国家呼吁更强的IPR保护，由于它对IPR的要求相对更高，也意味着它与研发能力较弱的国家在对IPR选择上，具有内在的冲突。

结论
IPR的国民待遇有利于促进小国的研发（或小国更欢迎具有互惠的IPR国民待遇）但也存在一些问题：如一些国家存在搭便车的动力，可能最终的均衡是每个国家只为本国的研发者提供保护；这种非对称均衡呼唤研发的统一化，但这种统一化可能引致IPR的过度保护，如一国内部的IPR保护完全可以为研发者收回投资；另外一种可能是，两国均不提供IPR保护，此时，统一的IPR可能会带来福利的增进。

如果引入政府支持的研发活动，由于这种活动所产生的研发成果不会产生垄断定价（但会带来更高的研发成本），且可以便利于国际间技术外溢，但一国政府通常不会考虑这种正的外部性，因而存在投资不足。这就解释了，在现实中，各国更多地依赖IP制度，而不是公共支持的研发，尽管后者在一定的参数空间中更具有优势。